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Paper IPaper I · General Mental Ability

Profit, Loss and Interest

Profit, loss and discount, simple interest, and compound interest, with worked examples and practice

CAPF wiki•5 min read•15 sections
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PaperPaper ISubjectGMASyllabusGeneral Mental Ability: quantitative aptitude including numerical abilityImportanceHigh
GMAQuantitative AptitudeProfit LossDiscountSimple InterestCompound InterestPaper 1

A commercial-arithmetic family built directly on percentages, so revise percentage ratio and average alongside it. The two halves are profit and loss (one-time transactions) and interest (money growing over time).

Core formulas: profit, loss and discount

Concept Formula
Profit Selling Price (SP) - Cost Price (CP), when SP > CP
Loss CP - SP, when CP > SP
Profit percent (Profit / CP) times 100
Loss percent (Loss / CP) times 100
SP from profit% CP times (1 + profit%/100)
SP from loss% CP times (1 - loss%/100)
Discount Marked Price (MP) - SP
Discount percent (Discount / MP) times 100
SP from discount MP times (1 - discount%/100)

Profit and loss percent are always calculated on the cost price unless stated otherwise. Discount percent is always on the marked price.

Core formulas: interest

Concept Formula
Simple Interest (SI) (P times R times T) / 100
Amount (simple) P + SI
Compound Amount (annual) P times (1 + R/100)T
Compound Interest (CI) Amount - P
CI half-yearly rate becomes R/2, time becomes 2T
CI quarterly rate becomes R/4, time becomes 4T

Here P is principal, R is rate percent per annum, T is time in years.

Useful difference (CI minus SI)

Period Difference (CI - SI)
2 years P times (R/100)2
3 years P times (R/100)2 times (3 + R/100)

Worked examples

Example 1: Profit percent

A trader buys a fan for Rs 1,200 and sells it for Rs 1,500. Find the profit percent.

Profit = 1500 - 1200 = 300. Profit percent = (300 / 1200) times 100 = 25%.

Example 2: SP from a given loss

An item costing Rs 800 is sold at a 15% loss. Find the selling price.

SP = 800 times (1 - 15/100) = 800 times 0.85 = Rs 680.

Example 3: Marked price, discount, and profit together

A shopkeeper marks a jacket at Rs 2,000 and offers a 10% discount. If the cost price is Rs 1,500, find the profit percent.

SP = 2000 times 0.9 = Rs 1,800. Profit = 1800 - 1500 = 300. Profit percent = (300 / 1500) times 100 = 20%.

Example 4: The equal profit-and-loss trap

A man sells two watches at Rs 990 each, gaining 10% on one and losing 10% on the other. Find the overall result.

When two items sell at the same price with the same gain% and loss%, there is always a net loss of (common percent)2 / 100. Net loss percent = (10)2 / 100 = 1%. So he makes a 1% loss overall.

Example 5: Simple interest

Find the simple interest on Rs 12,000 at 8% per annum for 3 years.

SI = (12000 times 8 times 3) / 100 = 288000 / 100 = Rs 2,880.

Example 6: Compound interest

Find the compound interest on Rs 10,000 at 10% per annum for 2 years, compounded annually.

Amount = 10000 times (1.1)2 = 10000 times 1.21 = Rs 12,100. CI = 12100 - 10000 = Rs 2,100.

Example 7: CI minus SI shortcut

What is the difference between CI and SI on Rs 5,000 at 10% for 2 years?

Difference = P times (R/100)2 = 5000 times (0.1)2 = 5000 times 0.01 = Rs 50.

Shortcut tips

  • Selling two articles at the same price, one at +x% and one at -x%, always loses x2/100 percent. Never zero.
  • For successive discounts of a% and b%, treat like successive percentage change: net = a + b - (ab/100) percent off.
  • Money doubles under simple interest in 100/R years; under compound interest, use the rule of 72 (time to double is about 72/R years).
  • For 2-year CI, the quick check is Amount = P times (1 + R/100)2; expand (1 + r)2 = 1 + 2r + r2 to do it mentally.
  • Always set profit and loss on CP, and discount on MP; mixing the base is the most common error.

Practice questions

  1. An item costs Rs 500 and sells for Rs 575. Find the profit percent.
  2. A book is sold for Rs 360 at a 20% profit. Find the cost price.
  3. A cycle marked at Rs 4,000 is sold at a 12% discount. Find the selling price.
  4. Two successive discounts of 20% and 10% are given on Rs 1,000. Find the final price.
  5. Find the SI on Rs 8,000 at 6% per annum for 4 years.
  6. In how many years will Rs 2,000 become Rs 2,600 at 10% simple interest?
  7. Find the compound amount on Rs 16,000 at 25% per annum for 2 years.
  8. A man sells two phones at Rs 1,200 each, one at 20% profit and one at 20% loss. Find his net loss percent.
  9. Find the difference between CI and SI on Rs 8,000 at 5% for 2 years.
  10. A trader buys at Rs 90 and wants 25% profit. At what price should he sell?

Answer key

Reveal the answer key and full worked solutions
  1. Profit 75, percent = (75/500) times 100 = 15%.
  2. CP = 360 / 1.2 = Rs 300.
  3. SP = 4000 times 0.88 = Rs 3,520.
  4. 1000 times 0.8 times 0.9 = Rs 720.
  5. SI = (8000 times 6 times 4)/100 = Rs 1,920.
  6. SI = 600 = (2000 times 10 times T)/100 = 200T, so T = 3 years.
  7. Amount = 16000 times (1.25)2 = 16000 times 1.5625 = Rs 25,000.
  8. Net loss = (20)2/100 = 4%.
  9. Difference = 8000 times (0.05)2 = 8000 times 0.0025 = Rs 20.
  10. SP = 90 times 1.25 = Rs 112.50.

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