Profit and Loss

Competitive Mathematics · Arithmetic

6 Part5 worked examples26 practice questions

A vegetable seller buys tomatoes at ₹20 a kg and sells at ₹26 — a profit of ₹6 on every kg. If some go bad and must go for ₹15 a kg that is a loss of ₹5. The whole chapter is the accounting of that everyday thing: what you put in, what you got back, and by what per cent the two differ. Keep one rule firm — profit or loss per cent is always on the cost price, unless the question says otherwise.

लाभ % = \frac{लाभ}{क्रय मूल्य} \times 100, हानि % = \frac{हानि}{क्रय मूल्य} \times 100

The most basic formulas

Basic terms and formulas

CP · SP · profit · loss

Cost price, selling price, profit and loss, and finding the per cent.

The terms and core formulas

Everything relative to the cost price

CP, SP, overheads, profit, loss, and SP = CP × factor.

Term	Meaning
Cost price (CP)	the price at which an article is bought or made
Selling price (SP)	the price at which it is sold
Overhead charges	freight, rent, repairs and similar extras — added to the CP; ignored if the question does not mention them
Profit	SP > CP; profit = SP − CP
Loss	CP > SP; loss = CP − SP

SP = CP \times \frac{100 + g}{100} (लाभ g %), SP = CP \times \frac{100 - l}{100} (हानि l %)

The multiplier form — the most useful

“45% profit” means SP = 145% of CP, a multiplier of 1.45. “25% loss” means SP = 75% of CP, a multiplier of 0.75. Finding CP is just as easy: CP = SP ÷ multiplier.

Example 1 · Basic

A book bought for ₹240 was sold for ₹300. Find the profit and the profit per cent.

Solution, step by step

1Profit $= 300 - 240 = 60$ .
2Profit $% = \frac{60}{240} \times 100 = 25%$

Answer ₹60 and 25%

Example 2 · Basic

A table lamp was bought for ₹650. What is its SP at a 12% profit?

Solution, step by step

1Multiplier $= \frac{112}{100}$ .
2SP $= 650 \times 1.12 = 728$

Answer ₹728

Example 3 · Standard

A pair of shoes was sold at a 15% loss for ₹1,530. What was the cost price?

Solution, step by step

1SP $= 85%$ of CP ⟹ CP $= \frac{1530 \times 100}{85}$ .
2 $= 1800$

Answer ₹1,800

Finding profit, loss, SP and CP

Four jobs, one multiplier

Per cent, SP and CP — all three kinds of direct questions, and questions with overheads.

Example 4 · Standard

A watch sold for ₹1,350 incurs a 10% loss. At what price should it be sold to gain 10%?

Solution, step by step

1CP $= \frac{1350 \times 100}{90} = 1500$ .
2New SP $= 1500 \times 1.10 = 1650$

Answer ₹1,650

The CP does not change — find it first.

Example 5 · Standard

A second-hand bicycle was bought for ₹2,400, ₹600 went on painting and repairs, and it sold for ₹3,450. What is the profit per cent?

Solution, step by step

1Total cost $= 2400 + 600 = 3000$ .
2Profit $= 3450 - 3000 = 450$ ⟹ $\frac{450}{3000} \times 100 = 15%$

Answer 15%

BasicTry it yourself first

An article bought for ₹480 was sold for ₹540. What is the profit?

BasicTry it yourself first

An article bought for ₹1,250 was sold for ₹1,100. What is the loss?

BasicTry it yourself first

An article bought for ₹200 is sold for ₹250. What is the profit per cent?

BasicTry it yourself first

An article bought for ₹800 is sold for ₹720. What is the loss per cent?

StandardTry it yourself first

An article bought for ₹1,250 is sold for ₹1,400. What is the profit per cent?

StandardTry it yourself first

An article bought for ₹3,600 is sold for ₹3,150. What is the loss per cent?

AdvancedTry it yourself first

An article bought for ₹4,500 is sold for ₹5,265. What is the profit per cent?

BasicTry it yourself first

The cost price is ₹500 and there is a 20% profit. What is the selling price?

BasicTry it yourself first

The cost price is ₹800 and there is a 15% loss. What is the selling price?

StandardTry it yourself first

The cost price is ₹3,200 and there is a 12.5% profit. What is the selling price?

StandardTry it yourself first

The cost price is ₹4,800 and there is a 7.5% loss. What is the selling price?

AdvancedTry it yourself first

The cost price is ₹7,600 and there is a 18% profit. What is the selling price?

BasicTry it yourself first

An article sold for ₹1,320 gives a 10% profit. What was its cost price?

StandardTry it yourself first

An article sold for ₹2,040 gives a 15% loss. What was its cost price?

StandardTry it yourself first

An article sold for ₹3,150 gives a 5% profit. What was its cost price?

AdvancedTry it yourself first

An article sold for ₹5,832 gives a 4% loss. What was its cost price?

AdvancedTry it yourself first

An article sold for ₹8,190 gives a 30% profit. What was its cost price?

StandardTry it yourself first

A watch sold for ₹1,620 gives a 10% loss. At what price should it be sold for a 12% profit?

StandardTry it yourself first

A watch sold for ₹2,640 gives a 10% profit. At what price should it be sold for a 5% loss?

AdvancedTry it yourself first

A watch sold for ₹1,196 gives a 8% loss. At what price should it be sold for a 15% profit?

StandardTry it yourself first

A second-hand scooter was bought for ₹4,000, ₹500 was spent on repairs and it was sold for ₹5,400. What is the profit per cent?

AdvancedTry it yourself first

A second-hand scooter was bought for ₹12,500, ₹1,500 was spent on repairs and it was sold for ₹12,600. What is the loss per cent?

StandardTry it yourself first

The profit on an article is 20% of its selling price. What is the profit per cent on the cost price?

AdvancedTry it yourself first

The profit on an article is 37.5% of its selling price. What is the profit per cent on the cost price?

StandardTry it yourself first

The ratio of the cost price to the selling price of an article is 5 : 6. What is the profit per cent?

AdvancedTry it yourself first

The ratio of the cost price to the selling price of an article is 8 : 7. What is the loss per cent?

Two articles, rates and weights

Deals with one handy trick

Gain on one and loss on the other, “CP = SP”, rates per rupee and false weights.

Gain on one, loss on the other

Equal SP always means a loss

When two articles are sold at the same price, one at $a %$ profit and the other at $a %$ loss.

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“CP = SP” and rates per rupee

Use one common number

When the CP of $a$ articles equals the SP of $b$ , or articles are bought and sold at “so many per rupee”.

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False weights

Profit on the weight actually given

A dishonest dealer’s profit when he sells at cost price but weighs short.

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Mixtures, chains and extra amounts

The exam favourites

Selling a mixture, passing through many hands, breaking even after selling part at a loss, and the “had it sold for more…” questions.

Mixtures and chains

Total CP, total SP

Add the costs when mixing; multiply the factors when it changes hands.

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“Had it sold for more…” and break-even

The money value of the gap in per cents

The gap between two per cents equals the extra money.

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Traps and fast tricks

Slips · the power of the multiplier

Where most marks leak in profit and loss and how to prevent it.

The commonest mistakes

Six traps

The slips that cost marks.

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Fast tricks

Multipliers · assume 100 · ratios

Habits that shorten the work.

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The practice ladder

Basic → standard → advanced

New questions of every type, in three levels.

Level 1 — Basic

Direct rules

One-rule questions.

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Level 2 — Standard

Two ideas combined

Exam-level questions.

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Level 3 — Advanced

Many steps and clever thinking

Questions at the hard end of competitive exams.

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Revision — formula cards

Flip each card and test yourself

Read the front, think, then flip.

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Profit and Loss

Basic terms and formulas

The terms and core formulas

Finding profit, loss, SP and CP

Two articles, rates and weights

Gain on one, loss on the other

“CP = SP” and rates per rupee

False weights

Mixtures, chains and extra amounts

Mixtures and chains

“Had it sold for more…” and break-even

Traps and fast tricks

The commonest mistakes

Fast tricks

The practice ladder

Level 1 — Basic

Level 2 — Standard

Level 3 — Advanced

Revision — formula cards

Free All Access Passevery mind map · Hindi + English · 12 months

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