Profit and Loss — Extra Practice

Competitive Mathematics · Arithmetic

6 Part15 worked examples142 practice questions

NoteThis is the Extra Practice set: lots of questions. To learn the methods first, read the main chapter of the same topic (the one without “Extra Practice” in its name), then practise here.

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.

∑ Formula

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

∑ Formula

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.

∑ Formula

हानि % = \frac{a ^{2}}{100} (जब दोनों का SP बराबर और लाभ - हानि समान a %)

The two-article rule

Why? The article sold at an $a %$ gain had a smaller cost, and the one at an $a %$ loss a larger cost. The loss falls on the bigger cost, the gain on the smaller — so there is a net loss. Note the formula does not need the SP.

Example 6 · Standard

A trader sold two mattresses at ₹3,000 each — one at a 25% gain, the other at a 25% loss. What is the net gain or loss?

Solution, step by step

1First CP $= \frac{3000 \times 100}{125} = 2400$ ; second $= \frac{3000 \times 100}{75} = 4000$ .
2Total CP $= 6400$ , total SP $= 6000$ ⟹ loss ₹400 $= \frac{2 5 ^{2}}{100} % = 6.25%$ of ₹6,400 ✓

Answer ₹400 loss (6.25%)

BasicTry it yourself first

A man sold two radios at ₹1,500 each — one at a 10% gain and the other at a 10% loss. What is his gain or loss per cent on the whole deal?

StandardTry it yourself first

A man sold two radios at ₹2,400 each — one at a 20% gain and the other at a 20% loss. What is his gain or loss per cent on the whole deal?

StandardTry it yourself first

A man sold two radios at ₹3,600 each — one at a 30% gain and the other at a 30% loss. What is his gain or loss per cent on the whole deal?

AdvancedTry it yourself first

A man sold two radios at ₹4,800 each — one at a 15% gain and the other at a 15% loss. What is his gain or loss per cent on the whole deal?

“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”.

∑ Formula

लाभ % = \frac{a - b}{b} \times 100 (CP_{a} = SP_{b})

The equal-value rule

Example 7 · Basic

If the cost price of 30 pens equals the selling price of 25 pens, what is the profit per cent?

Solution, step by step

1Let each pen cost ₹1; the SP of 25 pens = CP of 30 pens = ₹30.
2SP of one pen $= \frac{30}{25} = 1.2$ ⟹ profit 20%

Answer 20%

Example 8 · Standard

A seller buys 8 eggs for ₹10 and sells 6 eggs for ₹10. What is his profit per cent?

Solution, step by step

1Take 24 eggs: CP $= \frac{24}{8} \times 10 = 30$ , SP $= \frac{24}{6} \times 10 = 40$ .
2Profit $= \frac{10}{30} \times 100 = 33 \frac{1}{3} %$

Answer $33 \frac{1}{3} %$

BasicTry it yourself first

The cost price of 24 articles equals the selling price of 20 articles. What is the profit per cent?

StandardTry it yourself first

The cost price of 45 articles equals the selling price of 36 articles. What is the profit per cent?

StandardTry it yourself first

The cost price of 18 articles equals the selling price of 24 articles. What is the loss per cent?

AdvancedTry it yourself first

The cost price of 63 articles equals the selling price of 54 articles. What is the profit per cent?

BasicTry it yourself first

A hawker buys fruit at 5 for ₹1 and sells at 4 for ₹1. What is the profit per cent?

StandardTry it yourself first

A hawker buys fruit at 12 for ₹1 and sells at 10 for ₹1. What is the profit per cent?

StandardTry it yourself first

A hawker buys fruit at 6 for ₹1 and sells at 8 for ₹1. What is the loss per cent?

AdvancedTry it yourself first

A hawker buys fruit at 15 for ₹5 and sells at 12 for ₹5. What is the profit per cent?

False weights

Profit on the weight actually given

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

∑ Formula

लाभ % = \frac{सही वज़न - इस्तेमाल किया वज़न}{इस्तेमाल किया वज़न} \times 100

The false-weight formula

The profit is on the weight the customer actually gets, because the dealer paid only for that much stock. If the dealer claims a $a %$ gain or loss and also weighs short, multiply the two factors: real factor $= \frac{100 \pm a}{100} \times \frac{weight claimed}{weight given}$ .

Example 9 · Standard

A dealer claims to sell at cost but gives 800 g for 1 kg. What is his profit per cent?

Solution, step by step

1Profit $= \frac{1000 - 800}{800} \times 100$ .
2 $= 25%$

Answer 25%

Example 10 · Advanced

A dealer allows a 10% discount on cost but gives 900 g for 1 kg. What is his profit or loss per cent?

Solution, step by step

1Let 1 kg cost ₹100; he takes ₹90 (10% below cost) and gives 900 g, whose cost is ₹90.
2Profit $= 90 - 90 = 0$ ⟹ neither gain nor loss

Answer 0% (neither gain nor loss)

BasicTry it yourself first

A dishonest dealer claims to sell at cost price but uses 625 g for 1 kg. What is his gain per cent?

StandardTry it yourself first

A dishonest dealer claims to sell at cost price but uses 500 g for 1 kg. What is his gain per cent?

StandardTry it yourself first

A dishonest dealer claims to sell at cost price but uses 640 g for 1 kg. What is his gain per cent?

AdvancedTry it yourself first

A dishonest dealer claims to sell at cost price but uses 400 g for 1 kg. What is his gain per cent?

AdvancedTry it yourself first

A dishonest dealer claims to sell at cost price but uses 250 g for 1 kg. What is his gain per cent?

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.

Example 11 · Standard

A trader bought 40 kg of sugar at ₹36/kg and 60 kg at ₹41/kg and mixed them. At what rate per kg should he sell the mixture for a 15% profit?

Solution, step by step

1Total CP $= 1440 + 2460 = 3900$ ; total SP $= 3900 \times 1.15 = 4485$ .
2Per kg $= \frac{4485}{100} = 44.85$

Answer ₹44.85

Example 12 · Standard

Priya sold a cupboard to Rohan at a 20% profit and Rohan sold it to Meena at a 10% loss. Meena paid ₹5,400. What was Priya’s cost?

Solution, step by step

1Factor $= 1.20 \times 0.90 = 1.08$ .
2Priya’s CP $= \frac{5400}{1.08} = 5000$

Answer ₹5,000

BasicTry it yourself first

A grocer mixes 20 kg of rice at ₹30/kg with 30 kg at ₹40/kg. At what rate per kg must he sell the mixture to gain 20% on the whole?

StandardTry it yourself first

A grocer mixes 25 kg of rice at ₹24/kg with 15 kg at ₹40/kg. At what rate per kg must he sell the mixture to gain 25% on the whole?

AdvancedTry it yourself first

A grocer mixes 35 kg of rice at ₹42/kg with 45 kg at ₹52/kg. At what rate per kg must he sell the mixture to gain 12% on the whole?

BasicTry it yourself first

Aman bought a machine for ₹4,000 and sold it to Bala at a 10% profit. Bala sold it to Chetan at a 20% profit. For how much did Chetan buy it?

StandardTry it yourself first

Aman bought a machine for ₹6,000 and sold it to Bala at a 20% profit. Bala sold it to Chetan at a 10% loss. For how much did Chetan buy it?

StandardTry it yourself first

Aman bought a machine for ₹7,500 and sold it to Bala at a 20% loss. Bala sold it to Chetan at a 25% profit. For how much did Chetan buy it?

AdvancedTry it yourself first

Aman bought a machine for ₹12,500 and sold it to Bala at a 12% profit. Bala sold it to Chetan at a 8% loss. For how much did Chetan buy it?

AdvancedTry it yourself first

Aman bought a machine for ₹9,000 and sold it to Bala at a 10% loss. Bala sold it to Chetan at a 10% loss. For how much did Chetan buy it?

“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.

If both are profits: extra money $= (b - a) %$ of CP. If one is a loss and the other a profit: extra money $= (a + b) %$ of CP. So CP $= \frac{extra money \times 100}{difference or sum of the per cents}$ . In break-even questions write amount of loss = amount of gain.

Example 13 · Standard

A table is sold at an 8% profit. Had it sold for ₹360 more the profit would be 14%. What is its CP?

Solution, step by step

1The extra ₹360 $= (14 - 8) % = 6%$ of CP.
2CP $= \frac{360 \times 100}{6} = 6000$

Answer ₹6,000

Example 14 · Advanced

A trader bought stock worth ₹9,000 and sold

\frac{1}{3}

of it at a 24% loss. At what gain on the rest will he neither gain nor lose overall?

Solution, step by step

1CP of the part sold ₹3,000, loss $= 24% \times 3000 = 720$ .
2On the remaining CP of ₹6,000 a gain of ₹720 ⟹ $\frac{720}{6000} \times 100 = 12%$

Answer 12%

BasicTry it yourself first

An article is sold at a 10% profit. Had it been sold for ₹150 more the profit would have been 16%. What is its cost price?

StandardTry it yourself first

An article is sold at a 5% profit. Had it been sold for ₹360 more the profit would have been 12.5%. What is its cost price?

AdvancedTry it yourself first

An article is sold at a 12% profit. Had it been sold for ₹468 more the profit would have been 18.5%. What is its cost price?

StandardTry it yourself first

An article is sold at a 8% loss. Had it fetched ₹300 more there would have been a 12% profit. What is its cost price?

AdvancedTry it yourself first

An article is sold at a 15% loss. Had it fetched ₹900 more there would have been a 10% profit. What is its cost price?

AdvancedTry it yourself first

An article is sold at a 12.5% loss. Had it fetched ₹840 more there would have been a 7.5% profit. What is its cost price?

StandardTry it yourself first

A shopkeeper sold

\frac{1}{3}

of his stock at a 30% loss. At what gain per cent must he sell the rest to neither gain nor lose?

StandardTry it yourself first

A shopkeeper sold

\frac{1}{4}

of his stock at a 12% loss. At what gain per cent must he sell the rest to neither gain nor lose?

AdvancedTry it yourself first

A shopkeeper sold

\frac{2}{5}

of his stock at a 18% loss. At what gain per cent must he sell the rest to neither gain nor lose?

AdvancedTry it yourself first

A shopkeeper sold

\frac{3}{7}

of his stock at a 28% loss. At what gain per cent must he sell the rest to neither gain nor lose?

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.

Trap 1Taking the per cent on the SP. For ₹80 bought and ₹100 sold the profit is

\frac{20}{80} = 25%

, not

\frac{20}{100} = 20%

Trap 2Thinking a 10% gain followed by a 10% loss cancels.

1.10 \times 0.90 = 0.99

— a net 1% loss.

Trap 3Calling an equal gain and loss on two articles zero. At equal SPs there is always an

\frac{a ^{2}}{100} %

loss.

Trap 4Subtracting the overheads. Repair and freight costs are added to the CP.

Trap 5Using the wrong divisor with false weights. The divisor is the weight the customer actually gets, not 1000 g.

Trap 6Multiplying to find CP. To get CP, divide the SP by the multiplier; multiplying lands you among the trap options.

Fast tricks

Multipliers · assume 100 · ratios

Habits that shorten the work.

Think in multipliers: 20% profit = ×1.2, 15% loss = ×0.85, 12.5% profit = × $\frac{9}{8}$ .
Assume CP = 100 when no amount is given — then per cent becomes money directly.
Fraction form: 12.5% $= \frac{1}{8}$ , 16.67% $= \frac{1}{6}$ , 33.33% $= \frac{1}{3}$ , 20% $= \frac{1}{5}$ . If the profit is $\frac{1}{n}$ then CP : SP $= n : (n + 1)$ .
Successive changes: the net effect of $a %$ and $b %$ is $a + b + \frac{ab}{100}$ (use a minus for a loss).
Multiply the two factors; do not add the percents.

Example 15 · Standard

What is the net effect of a 20% profit followed by a 15% loss?

Solution, step by step

1Factor $= 1.20 \times 0.85 = 1.02$ .
2So a net profit of 2%. (Formula: $20 - 15 - \frac{20 \times 15}{100} = 2$ )

Answer 2% profit

The practice ladder

Basic → standard → advanced

New questions of every type, in three levels.

Level 1 — Basic

Direct rules

One-rule questions.

BasicTry it yourself first

An article bought for ₹360 was sold for ₹420. What is the profit?

BasicTry it yourself first

An article bought for ₹950 was sold for ₹800. What is the loss?

BasicTry it yourself first

An article bought for ₹400 is sold for ₹500. What is the profit per cent?

BasicTry it yourself first

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

BasicTry it yourself first

The cost price is ₹900 and there is a 10% profit. What is the selling price?

BasicTry it yourself first

The cost price is ₹640 and there is a 25% loss. What is the selling price?

BasicTry it yourself first

An article sold for ₹1,380 gives a 15% profit. What was its cost price?

BasicTry it yourself first

An article sold for ₹900 gives a 10% loss. What was its cost price?

BasicTry it yourself first

A man sold two radios at ₹1,800 each — one at a 20% gain and the other at a 20% loss. What is his gain or loss per cent on the whole deal?

BasicTry it yourself first

The cost price of 36 articles equals the selling price of 30 articles. What is the profit per cent?

BasicTry it yourself first

A hawker buys fruit at 10 for ₹1 and sells at 8 for ₹1. What is the profit per cent?

BasicTry it yourself first

A dishonest dealer claims to sell at cost price but uses 750 g for 1 kg. What is his gain per cent?

BasicTry it yourself first

Aman bought a machine for ₹2,000 and sold it to Bala at a 20% profit. Bala sold it to Chetan at a 10% profit. For how much did Chetan buy it?

BasicTry it yourself first

A grocer mixes 10 kg of rice at ₹20/kg with 15 kg at ₹30/kg. At what rate per kg must he sell the mixture to gain 20% on the whole?

BasicTry it yourself first

An article is sold at a 5% profit. Had it been sold for ₹60 more the profit would have been 10%. What is its cost price?

BasicTry it yourself first

A shopkeeper sold

\frac{1}{2}

of his stock at a 10% loss. At what gain per cent must he sell the rest to neither gain nor lose?

BasicTry it yourself first

The ratio of the cost price to the selling price of an article is 4 : 5. What is the profit per cent?

BasicTry it yourself first

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

BasicTry it yourself first

A watch sold for ₹880 gives a 12% loss. At what price should it be sold for a 5% profit?

BasicTry it yourself first

A second-hand scooter was bought for ₹800, ₹100 was spent on repairs and it was sold for ₹990. What is the profit per cent?

Level 2 — Standard

Two ideas combined

Exam-level questions.

StandardTry it yourself first

An article bought for ₹2,400 is sold for ₹2,700. What is the profit per cent?

StandardTry it yourself first

An article bought for ₹1,800 is sold for ₹1,530. What is the loss per cent?

StandardTry it yourself first

The cost price is ₹2,750 and there is a 18% profit. What is the selling price?

StandardTry it yourself first

The cost price is ₹6,400 and there is a 12.5% loss. What is the selling price?

StandardTry it yourself first

An article sold for ₹4,620 gives a 10% profit. What was its cost price?

StandardTry it yourself first

An article sold for ₹3,315 gives a 15% loss. What was its cost price?

StandardTry it yourself first

A watch sold for ₹3,150 gives a 10% loss. At what price should it be sold for a 20% profit?

StandardTry it yourself first

A watch sold for ₹4,980 gives a 20% profit. At what price should it be sold for a 5% profit?

StandardTry it yourself first

A man sold two radios at ₹2,800 each — one at a 25% gain and the other at a 25% loss. What is his gain or loss per cent on the whole deal?

StandardTry it yourself first

A man sold two radios at ₹5,400 each — one at a 10% gain and the other at a 10% loss. What is his gain or loss per cent on the whole deal?

StandardTry it yourself first

The cost price of 30 articles equals the selling price of 24 articles. What is the profit per cent?

StandardTry it yourself first

The cost price of 40 articles equals the selling price of 32 articles. What is the profit per cent?

StandardTry it yourself first

A hawker buys fruit at 9 for ₹1 and sells at 6 for ₹1. What is the profit per cent?

StandardTry it yourself first

A hawker buys fruit at 20 for ₹1 and sells at 25 for ₹1. What is the loss per cent?

StandardTry it yourself first

A dishonest dealer claims to sell at cost price but uses 840 g for 1 kg. What is his gain per cent?

StandardTry it yourself first

A dishonest dealer claims to sell at cost price but uses 920 g for 1 kg. What is his gain per cent?

StandardTry it yourself first

A grocer mixes 30 kg of rice at ₹28/kg with 20 kg at ₹38/kg. At what rate per kg must he sell the mixture to gain 15% on the whole?

StandardTry it yourself first

A grocer mixes 45 kg of rice at ₹32/kg with 35 kg at ₹44/kg. At what rate per kg must he sell the mixture to gain 10% on the whole?

StandardTry it yourself first

Aman bought a machine for ₹8,000 and sold it to Bala at a 15% profit. Bala sold it to Chetan at a 20% profit. For how much did Chetan buy it?

StandardTry it yourself first

Aman bought a machine for ₹5,600 and sold it to Bala at a 25% loss. Bala sold it to Chetan at a 15% profit. For how much did Chetan buy it?

StandardTry it yourself first

Aman bought a machine for ₹3,200 and sold it to Bala at a 25% profit. Bala sold it to Chetan at a 20% loss. For how much did Chetan buy it?

StandardTry it yourself first

An article is sold at a 9% profit. Had it been sold for ₹180 more the profit would have been 15%. What is its cost price?

StandardTry it yourself first

An article is sold at a 4% profit. Had it been sold for ₹520 more the profit would have been 12%. What is its cost price?

StandardTry it yourself first

An article is sold at a 10% loss. Had it fetched ₹600 more there would have been a 15% profit. What is its cost price?

StandardTry it yourself first

An article is sold at a 6% loss. Had it fetched ₹360 more there would have been a 14% profit. What is its cost price?

StandardTry it yourself first

A shopkeeper sold

\frac{1}{5}

of his stock at a 20% loss. At what gain per cent must he sell the rest to neither gain nor lose?

StandardTry it yourself first

A shopkeeper sold

\frac{2}{3}

of his stock at a 15% loss. At what gain per cent must he sell the rest to neither gain nor lose?

StandardTry it yourself first

A second-hand scooter was bought for ₹5,200, ₹800 was spent on repairs and it was sold for ₹7,200. What is the profit per cent?

StandardTry it yourself first

A second-hand scooter was bought for ₹7,500, ₹500 was spent on repairs and it was sold for ₹7,200. What is the loss per cent?

StandardTry it yourself first

The profit on an article is 25% 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 7 : 9. What is the profit per cent?

StandardTry it yourself first

The ratio of the cost price to the selling price of an article is 10 : 9. What is the loss per cent?

Level 3 — Advanced

Many steps and clever thinking

Questions at the hard end of competitive exams.

AdvancedTry it yourself first

An article bought for ₹3,750 is sold for ₹4,575. What is the profit per cent?

AdvancedTry it yourself first

The cost price is ₹12,600 and there is a 17.5% profit. What is the selling price?

AdvancedTry it yourself first

An article sold for ₹7,392 gives a 12% loss. What was its cost price?

AdvancedTry it yourself first

An article sold for ₹9,660 gives a 15% profit. What was its cost price?

AdvancedTry it yourself first

A watch sold for ₹4,410 gives a 16% loss. At what price should it be sold for a 24% profit?

AdvancedTry it yourself first

A man sold two radios at ₹7,200 each — one at a 40% gain and the other at a 40% loss. What is his gain or loss per cent on the whole deal?

AdvancedTry it yourself first

A man sold two radios at ₹6,300 each — one at a 35% gain and the other at a 35% loss. What is his gain or loss per cent on the whole deal?

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The cost price of 72 articles equals the selling price of 60 articles. What is the profit per cent?

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The cost price of 72 articles equals the selling price of 64 articles. What is the profit per cent?

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A hawker buys fruit at 7 for ₹1 and sells at 5 for ₹1. What is the profit per cent?

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A hawker buys fruit at 16 for ₹1 and sells at 14 for ₹1. What is the profit per cent?

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A dishonest dealer claims to sell at cost price but uses 800 g for 1 kg. What is his gain per cent?

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A dishonest dealer claims to sell at cost price but uses 640 g for 1 kg. What is his gain per cent?

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A grocer mixes 60 kg of rice at ₹34/kg with 40 kg at ₹49/kg. At what rate per kg must he sell the mixture to gain 18% on the whole?

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A grocer mixes 75 kg of rice at ₹28/kg with 25 kg at ₹56/kg. At what rate per kg must he sell the mixture to gain 22% on the whole?

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Aman bought a machine for ₹24,000 and sold it to Bala at a 25% profit. Bala sold it to Chetan at a 20% profit. For how much did Chetan buy it?

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Aman bought a machine for ₹15,000 and sold it to Bala at a 20% loss. Bala sold it to Chetan at a 10% loss. For how much did Chetan buy it?

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Aman bought a machine for ₹11,000 and sold it to Bala at a 18% profit. Bala sold it to Chetan at a 15% loss. For how much did Chetan buy it?

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An article is sold at a 7% profit. Had it been sold for ₹1,008 more the profit would have been 19%. What is its cost price?

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An article is sold at a 12.5% profit. Had it been sold for ₹825 more the profit would have been 20%. What is its cost price?

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An article is sold at a 12% loss. Had it fetched ₹1,600 more there would have been a 8% profit. What is its cost price?

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An article is sold at a 9.5% loss. Had it fetched ₹840 more there would have been a 5.5% profit. What is its cost price?

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A shopkeeper sold

\frac{3}{8}

of his stock at a 24% loss. At what gain per cent must he sell the rest to neither gain nor lose?

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A shopkeeper sold

\frac{4}{9}

of his stock at a 35% loss. At what gain per cent must he sell the rest to neither gain nor lose?

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A second-hand scooter was bought for ₹18,000, ₹2,000 was spent on repairs and it was sold for ₹25,000. What is the profit per cent?

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A second-hand scooter was bought for ₹26,500, ₹1,500 was spent on repairs and it was sold for ₹25,200. What is the loss per cent?

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

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The ratio of the cost price to the selling price of an article is 12 : 11. What is the loss per cent?

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The ratio of the cost price to the selling price of an article is 9 : 11. What is the profit per cent?

Revision — formula cards

Flip each card and test yourself

Read the front, think, then flip.