For Class 8, 9 & 10
Master the basics - and everything after gets easier
Concept-first questions with clear model answers in Physics, Chemistry, Maths and Biology, all NCERT-aligned. Start early, build the habit, and walk into your boards, NEET and JEE already ahead.
Interactive lessons
learn by playingDrag, slide and build - watch each concept come alive, then reveal the answer.
200 interactive lessons
Ohm's law
Class 10 Physics
Slide V & R, watch the bulb glow
Open →pH scale
Class 10 Chemistry
Slide across acids and bases
Open →Atomic number and mass number
Class 9 Chemistry
Add protons & neutrons, build shells
Open →Laws of reflection
Class 8 Physics
Change the angle, watch it bounce
Open →Volume of a sphere
Class 9 Maths
Grow the radius, see the volume
Open →Area of a trapezium
Class 8 Maths
Drag the sides, read the area
Open →Power of a lens
Class 10 Physics
Move the object, trace the rays
Open →Food chain and energy flow
Class 10 Biology
Follow the energy as it flows
Open →Speed
Class 8 Physics
Slide distance & time, watch the speed
Open →Density
Class 9 Physics
Pack mass into volume, float or sink
Open →Work done
Class 9 Physics
Push harder or farther, watch work grow
Open →Kinetic energy
Class 9 Physics
Speed it up - energy grows with the square
Open →Power of a lens
Class 10 Physics
Shorten the focal length, boost the power
Open →Mole concept
Class 9 Chemistry
Weigh out grams, count the moles
Open →Avogadro's number
Class 9 Chemistry
Add moles, count the particles
Open →Microscope magnification
Class 8 Biology
Grow the image, read the magnification
Open →Population density
Class 10 Biology
Add individuals, shrink the land, see crowding
Open →Simple interest
Class 8 Maths
Slide money, rate & time, watch interest
Open →Pythagoras theorem
Class 9 Maths
Stretch the two sides, get the hypotenuse
Open →Probability of an event
Class 10 Maths
Change the outcomes, watch the odds
Open →Newton's second law
Class 9 Physics
Push a mass, pick an acceleration
Open →Momentum
Class 9 Physics
Slide mass & velocity, build momentum
Open →Pressure
Class 8 Physics
Shrink the area, feel the pressure rise
Open →Weight
Class 9 Physics
Change the planet's gravity, watch your weight
Open →Refractive index
Class 10 Physics
Slow light in the medium, raise the index
Open →Resistors in series
Class 10 Physics
Add two resistors in a line
Open →Mass percentage of a solution
Class 9 Chemistry
Dissolve solute, read the strength
Open →Concentration of a solution
Class 9 Chemistry
Pack solute into less liquid
Open →Population change
Class 10 Biology
Balance births against deaths
Open →Compound microscope
Class 8 Biology
Combine eyepiece & objective lenses
Open →Area of a circle
Class 8 Maths
Grow the radius, watch the area square
Open →Volume of a cuboid
Class 8 Maths
Stretch length, breadth & height
Open →Electronic configuration and valency
Class 9 Chemistry
Slide the atomic number, build the atom
Open →Homologous series (alkanes)
Class 10 Chemistry
Add carbons, name the compound
Open →Mass number
Class 9 Chemistry
Add protons & neutrons, get the mass number
Open →Power
Class 9 Physics
More work in less time = more power
Open →Potential energy
Class 9 Physics
Lift a mass higher, store energy
Open →Wave speed
Class 9 Physics
Tune frequency & wavelength, set the speed
Open →Electric current
Class 10 Physics
Push charge per second, get the current
Open →Percentage
Class 8 Maths
Compare part to whole as a %
Open →Electron dot structure
Class 9 Chemistry
Draw valence electrons as dots
Open →Acceleration
Class 9 Physics
Speed up over time, find acceleration
Open →Distance, speed and time
Class 8 Physics
Set speed & time, cover the distance
Open →Frequency and time period
Class 9 Physics
Shorten the period, raise the frequency
Open →Heating effect of current
Class 10 Physics
Raise the current, watch heating soar
Open →Area of a triangle
Class 8 Maths
Set base & height, halve the rectangle
Open →Area of a rectangle
Class 8 Maths
Set length & breadth, fill the area
Open →Mean (average)
Class 9 Maths
Share the total equally across items
Open →Discount
Class 8 Maths
Slide price & % off, see the saving
Open →Heart rate
Class 10 Biology
Set heart rate & time, count the beats
Open →Resistors in parallel
Class 10 Physics
Wire two resistors side by side
Open →Electric charge
Class 10 Physics
Flow current over time, collect charge
Open →Electrical energy and units
Class 10 Physics
Run appliances, add up the units
Open →Kelvin temperature scale
Class 9 Chemistry
Slide Celsius, read the Kelvin
Open →Moles from number of particles
Class 9 Chemistry
Divide particles by Avogadro's number
Open →Ten percent law
Class 10 Biology
See 10% of energy reach the next level
Open →Area of a square
Class 8 Maths
Grow the side, square the area
Open →Volume of a cube
Class 8 Maths
Grow the edge, cube the volume
Open →Circumference of a circle
Class 8 Maths
Grow the radius, roll out the rim
Open →Surface area of a cube
Class 9 Maths
Grow the edge, cover six faces
Open →Potential difference
Class 10 Physics
Share work across charge, get volts
Open →Resistance from Ohm's law
Class 10 Physics
Divide voltage by current, get resistance
Open →Echo and SONAR
Class 9 Physics
Time the echo, find the distance
Open →Mass from moles
Class 9 Chemistry
Multiply moles by molar mass
Open →Breathing rate
Class 10 Biology
Set breathing rate & time
Open →Volume of a cylinder
Class 10 Maths
Set radius & height, fill the can
Open →Compound interest
Class 8 Maths
Compound money over years
Open →Profit and loss percentage
Class 8 Maths
Set cost & selling price, see profit %
Open →Perimeter of a rectangle
Class 8 Maths
Set length & breadth, walk the border
Open →Surface area of a sphere
Class 10 Maths
Grow the radius, wrap the ball
Open →Time period
Class 9 Physics
Raise the frequency, shrink the period
Open →Relative velocity
Class 9 Physics
Two objects approach - add their speeds
Open →Average velocity
Class 9 Physics
Average the start and end speeds
Open →Equations of motion (v = u + at)
Class 9 Physics
Accelerate from u for a time t
Open →Kelvin to Celsius
Class 9 Chemistry
Slide Kelvin, read the Celsius
Open →Population growth rate
Class 10 Biology
Balance births vs deaths per population
Open →Perimeter of a square
Class 8 Maths
Grow the side, walk four edges
Open →Perimeter of a triangle
Class 8 Maths
Add the three sides
Open →Area of a parallelogram
Class 8 Maths
Set base & height, slide the shape
Open →Area of a rhombus
Class 8 Maths
Set the two diagonals
Open →Equations of motion (distance)
Class 9 Physics
Start, accelerate, cover ground
Open →Joule's law of heating
Class 10 Physics
Raise current, resistance or time
Open →Electric power (P = VI)
Class 10 Physics
Multiply voltage by current
Open →Average atomic mass of isotopes
Class 9 Chemistry
Mix two isotopes by abundance
Open →Seed germination percentage
Class 9 Biology
Count sprouted seeds out of the total
Open →Volume of a cone
Class 9 Maths
Set radius & height, fill the cone
Open →Surface area of a cylinder
Class 9 Maths
Wrap the side and both ends
Open →Surface area of a cuboid
Class 9 Maths
Cover all six rectangular faces
Open →nth term of an AP
Class 10 Maths
Step from the first term by d
Open →Sum of an AP
Class 10 Maths
Add up the first n terms
Open →Focal length of a mirror
Class 10 Physics
Halve the radius to find the focus
Open →Speed of light in a medium
Class 10 Physics
Raise the index, slow the light
Open →Percentage purity
Class 9 Chemistry
Weigh the pure part of a sample
Open →Slope of a line
Class 10 Maths
Rise over run gives the steepness
Open →Percentage change
Class 8 Maths
Compare a new value to the old
Open →Volume of a hemisphere
Class 9 Maths
Grow the radius of half a ball
Open →Area of a sector
Class 10 Maths
Cut a slice of angle from a circle
Open →Length of an arc
Class 10 Maths
Measure the curved edge of a slice
Open →Slant height of a cone
Class 9 Maths
Combine radius & height for the slant
Open →Unit conversion (km/h to m/s)
Class 9 Physics
Convert km/h into m/s
Open →Equations of motion (v^2 = u^2 + 2as)
Class 9 Physics
Accelerate over a distance, find v
Open →Impulse
Class 9 Physics
Hit harder or longer, change momentum
Open →Wavelength
Class 9 Physics
Speed over frequency gives wavelength
Open →Oscillations
Class 9 Physics
Vibrate at a frequency for a time
Open →Cost of electricity
Class 10 Physics
Units times rate gives the bill
Open →Number of neutrons
Class 9 Chemistry
Take protons away from the mass number
Open →Curved surface area of a cone
Class 9 Maths
Wrap the slanted side of a cone
Open →Total surface area of a cone
Class 9 Maths
Add the base circle to the cone's side
Open →Curved surface area of a hemisphere
Class 9 Maths
Cover the dome of a hemisphere
Open →Diagonal of a square
Class 9 Maths
Cross a square corner to corner
Open →Unit conversion (m/s to km/h)
Class 9 Physics
Convert m/s into km/h
Open →Distance from velocities
Class 9 Physics
From two speeds, find the distance
Open →Diagonal of a rectangle
Class 9 Maths
Cross a rectangle corner to corner
Open →Diagonal of a cuboid
Class 9 Maths
The longest rod that fits in a box
Open →Area by Heron's formula
Class 9 Maths
Area from just the three sides
Open →Interior angle sum of a polygon
Class 8 Maths
Add up a polygon's inside angles
Open →Exterior angle of a regular polygon
Class 8 Maths
Share 360 among a polygon's corners
Open →Number of diagonals of a polygon
Class 8 Maths
Count the diagonals of a polygon
Open →Discriminant
Class 10 Maths
Test how many roots a quadratic has
Open →Sum of roots
Class 10 Maths
Sum of a quadratic's roots
Open →Punnett square (monohybrid cross)
Class 10 Biology
Cross two parents, predict the offspring
Open →Balancing chemical equations
Class 10 Chemistry
Slide coefficients until atoms balance
Open →Writing chemical formulae (valency)
Class 9 Chemistry
Criss-cross valencies into a formula
Open →Current from power
Class 10 Physics
Divide power by voltage for current
Open →Power (P = V^2 / R)
Class 10 Physics
Voltage squared over resistance
Open →Sine ratio
Class 10 Maths
Opposite over hypotenuse
Open →Cosine ratio
Class 10 Maths
Adjacent over hypotenuse
Open →Tangent ratio
Class 10 Maths
Opposite over adjacent
Open →Area of an equilateral triangle
Class 9 Maths
Area of an equilateral triangle
Open →Curved surface area of a cylinder
Class 9 Maths
Wrap only the curved side
Open →Loss percentage
Class 8 Maths
Sell below cost, find the loss %
Open →Amount with simple interest
Class 8 Maths
Principal plus its simple interest
Open →Distance formula
Class 10 Maths
Straight distance between two points
Open →States of matter
Class 9 Chemistry
Heat particles solid → liquid → gas
Open →Parts of a plant cell
Class 8 Biology
Tap a cell part to see its job
Open →Diagonal of a cube
Class 9 Maths
Longest diagonal through a cube
Open →Total surface area of a hemisphere
Class 9 Maths
Dome plus its flat circle
Open →Sum of first n natural numbers
Class 10 Maths
Add 1 + 2 + ... + n instantly
Open →Range of data
Class 9 Maths
Spread from smallest to largest
Open →Class mark
Class 9 Maths
Midpoint of a class interval
Open →Selling price from profit percent
Class 8 Maths
Mark up cost by a profit %
Open →Perimeter of a sector
Class 10 Maths
Two radii plus the curved arc
Open →Circumference from diameter
Class 8 Maths
Circumference straight from diameter
Open →Power (P = F x v)
Class 9 Physics
Force times velocity gives power
Open →Percentage of a number
Class 8 Maths
Find a percentage of a number
Open →Series and parallel circuits
Class 10 Physics
Break a bulb in series vs parallel
Open →Symbols of elements
Class 9 Chemistry
Match each element to its symbol
Open →Free fall (velocity)
Class 9 Physics
Drop from a height, hit this speed
Open →Free fall (time)
Class 9 Physics
How long a drop takes
Open →Free fall (distance)
Class 9 Physics
Distance fallen in a given time
Open →Complement of an event
Class 10 Maths
Chance an event does NOT happen
Open →Product of roots
Class 10 Maths
Product of a quadratic's roots
Open →Exterior angle theorem
Class 9 Maths
Exterior angle = sum of remote interiors
Open →Complementary angles
Class 10 Maths
What adds to 90 degrees
Open →Supplementary angles
Class 9 Maths
What adds to 180 degrees
Open →Perimeter of a semicircle
Class 10 Maths
Curved half plus the diameter
Open →Area of a semicircle
Class 10 Maths
Half the area of a circle
Open →Turning effect (moments)
Class 9 Physics
Balance the see-saw with moments
Open →Reflex arc
Class 10 Biology
Step through a reflex, stimulus to action
Open →Buoyant force (upthrust)
Class 9 Physics
Displace liquid, feel the upthrust
Open →Relative density
Class 9 Physics
Compare a density to water's
Open →Power in lifting a load
Class 9 Physics
Lift a load, faster needs more power
Open →Cosecant ratio
Class 10 Maths
Hypotenuse over opposite
Open →Secant ratio
Class 10 Maths
Hypotenuse over adjacent
Open →Cotangent ratio
Class 10 Maths
Adjacent over opposite
Open →Height from angle of elevation
Class 10 Maths
Height from an angle of elevation
Open →Area of a quadrant
Class 10 Maths
A quarter of a circle's area
Open →Interior angle of a regular polygon
Class 8 Maths
One inside angle of a regular polygon
Open →Sum of first n odd numbers
Class 10 Maths
Add the first n odd numbers
Open →Sum of first n even numbers
Class 10 Maths
Add the first n even numbers
Open →Quadratic formula (a root)
Class 10 Maths
Larger root of a quadratic
Open →LCM from HCF
Class 10 Maths
LCM from the product and HCF
Open →Depreciation
Class 8 Maths
Value drops by a % each year
Open →Cost price from selling price
Class 8 Maths
Work back to the cost price
Open →Downstream speed
Class 8 Maths
Row with the current
Open →Upstream speed
Class 8 Maths
Row against the current
Open →Average speed for a round trip
Class 8 Maths
Average speed there and back
Open →Sales tax / GST
Class 8 Maths
Tax added on a price
Open →Area of a ring (annulus)
Class 10 Maths
Area of a ring between two circles
Open →Edge of a cube from volume
Class 9 Maths
Edge back from the volume
Open →Radius from area
Class 10 Maths
Radius back from a circle's area
Open →Side from area of a square
Class 8 Maths
Side back from a square's area
Open →Height of a triangle from area
Class 9 Maths
Height back from area and base
Open →Rate from simple interest
Class 8 Maths
Rate back from the interest
Open →Time from simple interest
Class 8 Maths
Time back from the interest
Open →Principal from simple interest
Class 8 Maths
Principal back from the interest
Open →Mean proportional
Class 10 Maths
Geometric mean of two numbers
Open →Fourth proportional
Class 8 Maths
Complete the proportion a : b = c : ?
Open →Marked price from selling price
Class 8 Maths
Marked price back from the sale price
Open →Chambers of the human heart
Class 10 Biology
Tap a heart chamber to see its job
Open →Equation of a line (y = mx + c)
Class 9 Maths
Read y off a straight line
Open →Average term of an AP
Class 10 Maths
Average of first and last term
Open →Number of terms in an AP
Class 10 Maths
How many terms in an AP
Open →Midpoint of two points
Class 10 Maths
x-coordinate of a midpoint
Open →Empirical mode
Class 10 Maths
Estimate the mode from mean & median
Open →Length of a shadow
Class 10 Maths
Shadow from height and sun angle
Open →Train crossing a pole
Class 8 Maths
Speed to cross a pole
Open →Time and work
Class 8 Maths
More workers, fewer days
Open →Dividing in a ratio
Class 8 Maths
Split a total in a ratio
Open →Unitary method
Class 8 Maths
Cost of a single item
Open →Your progress — Foundation - Class 8 to 10
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Showing 23 questions for Class 8. Tap a card to reveal the answer.
MathematicsComparing QuantitieseasyA shopkeeper buys a bag for 500 rupees and sells it for 575 rupees. Find the profit percent.
Reveal answer ↓
What it is
Profit percent measures your gain compared with the cost price, not the selling price.
Answer
Profit = selling price - cost price = 575 - 500 = 75 rupees. Profit percent = (profit / cost price) x 100 = (75 / 500) x 100 = 15 percent. So the shopkeeper makes a 15 percent profit.
Profit% = (Profit / Cost Price) x 100
- •Profit = SP - CP = 75
- •Profit% = (Profit / CP) x 100
- •= (75/500) x 100 = 15%
Why learn this
It's the number every shop, startup and investor lives and dies by.
💡 Memory trick
Always divide by CP - the Cost Price is your 'Compare Point'.
MathematicsComparing QuantitieseasyFind the simple interest on 2000 at 5% per year for 3 years. Slide the values to explore.
Reveal answer ↓
What it is
Simple interest is the extra money paid for borrowing, or earned for saving, a sum.
Answer
Simple interest = P x R x T / 100 = 2000 x 5 x 3 / 100 = 300. So the interest is 300 in the same currency as the principal. Increasing the principal, the rate or the time each increases the interest.
SI = P x R x T / 100
- •SI = P x R x T / 100
- •P = principal, R = rate % per year, T = time in years
- •Interest grows with P, R and T
Why learn this
It's everyday money maths - loans, savings and deposits.
💡 Memory trick
SI = P x R x T / 100. More principal, rate or time -> more interest.
MathematicsComparing QuantitieseasyA student scores 45 out of 180. What percentage is that? Slide the values to explore.
Reveal answer ↓
What it is
A percentage expresses a part out of a whole as a number per hundred.
Answer
Percentage = (part / whole) x 100 = (45 / 180) x 100 = 25%. A percentage rescales any fraction to 'out of 100', which makes different quantities easy to compare.
percentage = (part / whole) x 100
- •% = (part / whole) x 100
- •It means 'per hundred'
- •45 out of 180 = 25%
Why learn this
It's how marks, discounts, interest and statistics are compared fairly.
💡 Memory trick
% = (part / whole) x 100.
MathematicsComparing QuantitieseasyA 2000 item has a 25% discount. How much do you save? Slide the values to explore.
Reveal answer ↓
What it is
A discount is a reduction on the marked price, found as a percentage of that price.
Answer
Discount = marked price x rate / 100 = 2000 x 25 / 100 = 500. So you save 500 and pay 2000 - 500 = 1500. A higher rate or a higher marked price gives a bigger saving.
discount = marked price x rate / 100
- •Discount = price x rate / 100
- •Final price = marked price - discount
- •Higher rate or price -> bigger saving
Why learn this
It's the maths behind every sale and offer.
💡 Memory trick
Discount = price x rate / 100. Pay = price - discount.
MathematicsComparing QuantitiesmediumFind the compound interest on 1000 at 10% per year for 2 years. Slide the values to explore.
Reveal answer ↓
What it is
Compound interest is calculated on the principal plus the interest already earned, so it grows faster than simple interest.
Answer
Amount A = P(1 + R/100)^T = 1000 x (1 + 10/100)^2 = 1000 x 1.21 = 1210. Compound interest = A - P = 1210 - 1000 = 210. This is more than the simple interest (200) because the second year's interest is earned on 1100, not just 1000.
A = P(1 + R/100)^T ; CI = A - P
- •A = P(1 + R/100)^T
- •CI = A - P
- •Interest is earned on interest, so it beats simple interest
Why learn this
It's how savings, loans and investments really grow over time.
💡 Memory trick
A = P(1 + R/100)^T, then CI = A - P.
MathematicsComparing QuantitieseasyAn item costing 2000 is sold for 2500. Find the profit percentage. Slide the values to explore.
Reveal answer ↓
What it is
Profit percentage is the profit expressed as a percentage of the cost price.
Answer
Profit = SP - CP = 2500 - 2000 = 500. Profit % = (profit / CP) x 100 = (500 / 2000) x 100 = 25%. The percentage is always taken on the cost price; if the selling price is below the cost price the answer is negative, showing a loss.
profit % = (SP - CP) / CP x 100
- •Profit % = (SP - CP) / CP x 100
- •Always taken on the cost price (CP)
- •A negative value means a loss
Why learn this
It's how shops and businesses measure how good a deal is.
💡 Memory trick
Profit % = (SP - CP) / CP x 100. Negative means a loss.
MathematicsComparing QuantitieseasyA value rises from 80 to 100. Find the percentage change. Slide the values to explore.
Reveal answer ↓
What it is
Percentage change is the increase or decrease compared with the original value, expressed as a percentage.
Answer
Percentage change = (new - old) / old x 100 = (100 - 80) / 80 x 100 = 20 / 80 x 100 = 25%. It is always taken on the original (old) value; if the new value is smaller, the change is negative, showing a decrease.
percentage change = (new - old) / old x 100
- •Change % = (new - old) / old x 100
- •Always on the old value
- •Negative means a decrease
Why learn this
It's how price rises, discounts and growth are reported.
💡 Memory trick
Change % = (new - old) / old x 100. Take it on the OLD value.
MathematicsComparing QuantitieseasyAn item costing 2000 is sold for 1600. Find the loss percentage. Slide the values to explore.
Reveal answer ↓
What it is
Loss percentage is the loss expressed as a percentage of the cost price.
Answer
Loss = CP - SP = 2000 - 1600 = 400. Loss % = (loss / CP) x 100 = (400 / 2000) x 100 = 20%. Like profit, it is always taken on the cost price; if the selling price is above the cost price, this becomes a profit instead.
loss % = (CP - SP) / CP x 100
- •Loss % = (CP - SP) / CP x 100
- •Always on the cost price
- •SP above CP means a profit
Why learn this
It measures how bad a deal is when something sells below cost.
💡 Memory trick
Loss % = (CP - SP) / CP x 100.
MathematicsComparing QuantitieseasyFind the amount on 2000 at 5% per year for 3 years. Slide the values to explore.
Reveal answer ↓
What it is
The amount to be repaid is the principal plus the simple interest earned on it.
Answer
Simple interest = P x R x T / 100 = 2000 x 5 x 3 / 100 = 300. Amount = principal + interest = 2000 + 300 = 2300. The amount is always the principal plus whatever interest has built up.
amount = P + (P x R x T / 100)
- •Amount = principal + simple interest
- •SI = P x R x T / 100
- •Amount = P + (P x R x T / 100)
Why learn this
It's the total you actually get back or pay after interest.
💡 Memory trick
Amount = P + (P x R x T / 100).
MathematicsComparing QuantitiesmediumAt what price should a 2000 item be sold to make a 25% profit? Slide to explore.
Reveal answer ↓
What it is
The selling price for a required profit is the cost price increased by that profit percentage.
Answer
SP = CP x (1 + profit% / 100) = 2000 x (1 + 25/100) = 2000 x 1.25 = 2500. The profit of 500 is 25% of the cost price, so the selling price is 2500.
SP = CP x (1 + profit% / 100)
- •SP = CP x (1 + profit% / 100)
- •Profit is taken on the cost price
- •25% on 2000 -> SP 2500
Why learn this
It's how a shopkeeper sets a price to earn a target profit.
💡 Memory trick
SP = CP x (1 + profit% / 100).
MathematicsComparing QuantitieseasyWhat is 20% of 150? Slide the values to explore.
Reveal answer ↓
What it is
A percentage of a number is that fraction out of a hundred, multiplied by the number.
Answer
Result = (percent / 100) x number = (20 / 100) x 150 = 0.2 x 150 = 30. Finding a percentage of a number just means multiplying the number by that fraction out of a hundred.
result = (percent / 100) x number
- •Result = (percent / 100) x number
- •20% of 150 = 30
- •Per cent means per hundred
Why learn this
It's used for discounts, tips, marks and shares of a quantity.
💡 Memory trick
Result = (percent / 100) x number.
MathematicsComparing QuantitiesmediumA 50000 machine depreciates 10% a year. Find its value after 2 years. Slide to explore.
Reveal answer ↓
What it is
Depreciation reduces an asset's value by a fixed percentage each year, like compound interest in reverse.
Answer
Value = P x (1 - r/100)^n = 50000 x (1 - 10/100)^2 = 50000 x 0.9^2 = 50000 x 0.81 = 40500. Each year the value becomes 90% of the previous year, so it falls faster at first.
value = P x (1 - r/100)^n
- •Value = P x (1 - r/100)^n
- •Compound decrease, not a flat subtraction
- •50000 at 10% -> 40500 after 2 years
Why learn this
It's how the value of vehicles and machines falls over time.
💡 Memory trick
Value = P x (1 - r/100)^n.
MathematicsComparing QuantitiesmediumAn item sold for 2500 at a 25% profit. Find the cost price. Slide to explore.
Reveal answer ↓
What it is
The cost price can be recovered from the selling price and the profit percentage by dividing.
Answer
CP = SP / (1 + profit% / 100) = 2500 / (1 + 25/100) = 2500 / 1.25 = 2000. Because the selling price is 125% of the cost price, we divide by 1.25 to get back to 100%.
CP = SP / (1 + profit% / 100)
- •CP = SP / (1 + profit% / 100)
- •SP is (100 + profit%) of CP
- •SP 2500 at 25% -> CP 2000
Why learn this
It's how you check what an item originally cost after a marked-up sale.
💡 Memory trick
CP = SP / (1 + profit% / 100).
MathematicsComparing QuantitieseasyFind the tax on a 1000 item at 12%. Slide the values to explore.
Reveal answer ↓
What it is
Sales tax is a percentage of the price added on top of it.
Answer
Tax = price x rate / 100 = 1000 x 12 / 100 = 120. The final amount paid is the price plus this tax, so 1000 + 120 = 1120.
tax = price x rate / 100
- •Tax = price x rate / 100
- •Added on top of the price
- •Final amount = price + tax
Why learn this
It's the GST added to almost everything you buy.
💡 Memory trick
Tax = price x rate / 100.
MathematicsComparing QuantitiesmediumAn interest of 300 comes from a principal of 2000 over 3 years. Find the rate. Slide to explore.
Reveal answer ↓
What it is
The rate of interest is found by rearranging the simple interest formula.
Answer
Rate = SI x 100 / (P x T) = 300 x 100 / (2000 x 3) = 30000 / 6000 = 5% per year. This is SI = P x R x T / 100 rearranged to make R the subject.
rate = SI x 100 / (P x T)
- •Rate = SI x 100 / (P x T)
- •Rearranged from SI = PRT/100
- •SI 300, P 2000, T 3 -> R 5%
Why learn this
It tells you what rate a deposit or loan is really charging.
💡 Memory trick
Rate = SI x 100 / (P x T).
MathematicsComparing QuantitiesmediumAn interest of 300 comes from a principal of 2000 at 5% per year. Find the time. Slide to explore.
Reveal answer ↓
What it is
The time is found by rearranging the simple interest formula.
Answer
Time = SI x 100 / (P x R) = 300 x 100 / (2000 x 5) = 30000 / 10000 = 3 years. This is SI = P x R x T / 100 rearranged to make T the subject.
time = SI x 100 / (P x R)
- •Time = SI x 100 / (P x R)
- •Rearranged from SI = PRT/100
- •SI 300, P 2000, R 5% -> T 3 years
Why learn this
It tells you how long money must stay invested to earn a given interest.
💡 Memory trick
Time = SI x 100 / (P x R).
MathematicsComparing QuantitiesmediumAn interest of 300 is earned at 5% per year for 3 years. Find the principal. Slide to explore.
Reveal answer ↓
What it is
The principal is found by rearranging the simple interest formula.
Answer
Principal = SI x 100 / (R x T) = 300 x 100 / (5 x 3) = 30000 / 15 = 2000. This is SI = P x R x T / 100 rearranged to make P the subject.
principal = SI x 100 / (R x T)
- •Principal = SI x 100 / (R x T)
- •Rearranged from SI = PRT/100
- •SI 300, R 5%, T 3 -> P 2000
Why learn this
It works out how much was invested to earn a known interest.
💡 Memory trick
Principal = SI x 100 / (R x T).
MathematicsComparing QuantitiesmediumAn item sold for 1500 after a 25% discount. Find the marked price. Slide to explore.
Reveal answer ↓
What it is
The marked price is recovered from the selling price and the discount percentage.
Answer
MP = SP / (1 - discount% / 100) = 1500 / (1 - 25/100) = 1500 / 0.75 = 2000. Because the selling price is 75% of the marked price, we divide by 0.75 to get back to the full price.
MP = SP / (1 - discount% / 100)
- •MP = SP / (1 - discount% / 100)
- •SP is (100 - discount%) of MP
- •SP 1500 at 25% off -> MP 2000
Why learn this
It tells you the original tag price before a discount.
💡 Memory trick
MP = SP / (1 - discount% / 100).
MathematicsComparing QuantitieseasyDivide 500 in the ratio 2 : 3. Find the first share. Slide the values to explore.
Reveal answer ↓
What it is
To divide a total in a given ratio, each share is the total times that part over the sum of the parts.
Answer
First share = total x a / (a + b) = 500 x 2 / (2 + 3) = 500 x 2 / 5 = 200. The second share is 500 x 3 / 5 = 300, and the two shares add back to 500.
share = total x part / sum of parts
- •First share = total x a / (a + b)
- •Shares add back to the total
- •500 in 2 : 3 -> 200 and 300
Why learn this
It's how money, sweets or profits are split fairly.
💡 Memory trick
First share = total x a / (a + b).
MathematicsComparing QuantitieseasyA student scored 45 marks out of 60. Find the percentage of marks.
Reveal answer ↓
What it is
A percentage is a fraction with denominator 100; it compares a part to a whole out of 100.
Answer
Percentage = (marks obtained / total marks) x 100 = (45/60) x 100 = 75%. So the student scored 75%.
Percentage = (part / whole) x 100
- •Percent = per hundred
- •Percentage = (part/whole) x 100
- •(45/60) x 100 = 75%
- •a% of b = (a/100) x b
Why learn this
Marks, discounts and interest are all expressed as percentages.
💡 Memory trick
Percent means 'per hundred'. To find a% of b, compute (a/100) x b.
MathematicsComparing QuantitiesmediumAn article bought for 500 rupees is sold for 600 rupees. Find the profit percent.
Reveal answer ↓
What it is
Profit or loss is always calculated as a percentage of the cost price.
Answer
Profit = selling price - cost price = 600 - 500 = 100 rupees. Profit percent = (profit / cost price) x 100 = (100/500) x 100 = 20%. So there is a 20% profit.
Profit% = (SP - CP)/CP x 100
- •Profit = SP - CP = 100
- •Profit% = (profit/CP) x 100
- •(100/500) x 100 = 20%
- •Always on cost price
Why learn this
Shopkeepers and buyers use it to know real gain or loss.
💡 Memory trick
Profit% and Loss% are BOTH found on Cost Price (CP), not selling price.
MathematicsComparing QuantitiesmediumThe marked price of a shirt is 800 rupees and a discount of 15% is given. Find the selling price.
Reveal answer ↓
What it is
A discount is a reduction given on the marked price of an article.
Answer
Discount = 15% of marked price = (15/100) x 800 = 120 rupees. Selling price = marked price - discount = 800 - 120 = 680 rupees. So the shirt is sold for 680 rupees.
SP = MP - discount ; discount = discount% of MP
- •Discount is on the marked price
- •Discount = (15/100) x 800 = 120
- •SP = MP - discount
- •SP = 800 - 120 = 680
Why learn this
It is how sale prices are calculated in shops.
💡 Memory trick
Discount is on the Marked Price (MP). Selling Price = MP - discount.
MathematicsComparing QuantitieshardFind the compound interest on 10000 rupees for 2 years at 10% per annum, compounded annually.
Reveal answer ↓
What it is
Compound interest is interest calculated on the amount, which grows each period as interest is added to the principal.
Answer
Using A = P(1 + R/100)^n, we get A = 10000 x (1 + 10/100)^2 = 10000 x (1.1)^2 = 10000 x 1.21 = 12100 rupees. Compound interest = A - P = 12100 - 10000 = 2100 rupees.
A = P(1 + R/100)^n ; CI = A - P
- •A = P(1 + R/100)^n
- •A = 10000 x (1.1)^2 = 12100
- •CI = A - P = 2100
- •Interest is added to principal each year
Why learn this
Banks and loans use compound interest, so it grows faster than simple interest.
💡 Memory trick
Amount A = P(1 + R/100)^n. Compound interest = A - P.
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