Partnership — Extra Practice

Competitive Mathematics · Arithmetic

6 Part13 worked examples115 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.

Two friends open a shop together — one puts in ₹1,00,000 and the other ₹2,00,000. If the year’s profit is ₹90,000, how is it split? The answer is the one idea of this chapter: each partner gets profit in proportion to the money he put in and how long it stayed. The ratio of profits equals the ratio of capital × time. If time is equal only the capital ratio matters; if capital is equal only the time ratio; if both differ, their product.

∑ Formula

P_{1} : P_{2} : P_{3} = C_{1} t_{1} : C_{2} t_{2} : C_{3} t_{3}

The profit ratio (capital × time)

Simple partnership

Either equal capital or equal time

When either capital or time is the same for all.

Equal time or equal capital

Whatever is equal cancels

If one factor is equal, profit follows the other.

Situation	Profit ratio
equal time, different capitals	$C_{1} : C_{2} : C_{3}$
equal capital, different times	$t_{1} : t_{2} : t_{3}$

Example 1 · Basic

A and B start a business with ₹30,000 and ₹50,000. The year’s profit is ₹72,000. Find their shares.

Solution, step by step

1Ratio $= 3 : 5$ ; total 8 parts, one part $= 9000$ .
2A gets ₹27,000; B ₹45,000.

Answer ₹27,000 and ₹45,000

Example 2 · Standard

Three partners put in ₹40,000 each. A stays 8 months, B 6 and C 12. What is C’s share of a ₹39,000 profit?

Solution, step by step

1Equal capital ⟹ ratio $= 8 : 6 : 12 = 4 : 3 : 6$ .
2C’s share $= 39000 \times \frac{6}{13} = 18000$

Answer ₹18,000

Example 3 · Basic

A’s investment is three times B’s. What is A’s share in an annual profit of ₹64,000?

Solution, step by step

1Ratio $3 : 1$ ; 4 parts; one part $= 16000$ .
2A’s share $= 3 \times 16000 = 48000$

Answer ₹48,000

BasicTry it yourself first

A invested ₹6,000, B invested ₹9,000 in a partnership and after 1 year the profit was ₹20,000. What is A's share?

BasicTry it yourself first

A invested ₹4,000, B invested ₹6,000, C invested ₹10,000 in a partnership and after 1 year the profit was ₹40,000. What is C's share?

StandardTry it yourself first

A invested ₹15,000, B invested ₹25,000, C invested ₹20,000 in a partnership and after 1 year the profit was ₹48,000. What is B's share?

AdvancedTry it yourself first

A invested ₹27,000, B invested ₹45,000, C invested ₹36,000, D invested ₹12,000 in a partnership and after 1 year the profit was ₹60,000. What is D's share?

BasicTry it yourself first

2 partners each put in ₹20,000 and stayed 3, 5 months respectively. The total profit is ₹24,000. What is B's share?

StandardTry it yourself first

3 partners each put in ₹30,000 and stayed 6, 9, 12 months respectively. The total profit is ₹54,000. What is C's share?

AdvancedTry it yourself first

3 partners each put in ₹45,000 and stayed 4, 7, 10 months respectively. The total profit is ₹63,000. What is B's share?

Sharing a loss

The same ratio, the other direction

A loss is shared in the same ratio as a profit.

In a loss every partner bears it in the ratio of capital × time. The one who put in more bears more. (Sometimes a question says a partner gives only labour — he does not bear the capital loss; read that condition carefully.)

Example 4 · Standard

A, B and C put in ₹20,000, ₹30,000 and ₹50,000. The business lost ₹15,000. What is B’s share of the loss?

Solution, step by step

1Ratio $= 2 : 3 : 5$ ; 10 parts; one part $= 1500$ .
2B’s loss $= 3 \times 1500 = 4500$

Answer ₹4,500

BasicTry it yourself first

A put in ₹8,000, B put in ₹12,000. The business lost ₹5,000. What is B's share of the loss?

StandardTry it yourself first

A put in ₹20,000, B put in ₹35,000, C put in ₹45,000. The business lost ₹20,000. What is C's share of the loss?

AdvancedTry it yourself first

A put in ₹24,000, B put in ₹30,000, C put in ₹36,000, D put in ₹60,000. The business lost ₹15,000. What is D's share of the loss?

Compound partnership

Different capitals and different times

Profit follows the products capital × time; joining later, changing capital and reversing the ratios.

Capital × time

“Capital-months”

Multiply each partner’s capital by his months and take the ratio.

Example 5 · Standard

A starts with ₹5,000 and B joins after 4 months with ₹9,000. The year’s profit is ₹33,000. Find the shares.

Solution, step by step

1A: $5000 \times 12 = 60000$ ; B: $9000 \times 8 = 72000$ ⟹ ratio $5 : 6$ .
2Total 11 parts; one part $= 3000$ ⟹ A ₹15,000, B ₹18,000.

Answer ₹15,000 and ₹18,000

Example 6 · Standard

A starts with ₹6,000 and B joins after 3 months with ₹8,000. The year’s profit is ₹34,500. Find the shares.

Solution, step by step

1A: $6000 \times 12 = 72000$ ; B: $8000 \times 9 = 72000$ ⟹ ratio $1 : 1$ .
2Each gets ₹17,250

Answer ₹17,250 each

Example 7 · Standard

A starts with ₹3,000, B joins after 3 months with ₹4,000 and C after 10 months with ₹9,000. Share the year’s profit of ₹65,000.

Solution, step by step

1A: $3000 \times 12 = 36000$ ; B: $4000 \times 9 = 36000$ ; C: $9000 \times 2 = 18000$ ⟹ $2 : 2 : 1$ .
2Total 5 parts; one part $= 13000$ ⟹ A ₹26,000, B ₹26,000, C ₹13,000.

Answer ₹26,000, ₹26,000, ₹13,000

BasicTry it yourself first

A put in ₹4,000 for 6 months, B put in ₹6,000 for 4 months. The total profit is ₹24,000. What is A's share?

StandardTry it yourself first

A put in ₹5,000 for 12 months, B put in ₹8,000 for 9 months, C put in ₹3,000 for 6 months. The total profit is ₹62,000. What is C's share?

AdvancedTry it yourself first

A put in ₹9,000 for 10 months, B put in ₹7,500 for 12 months, C put in ₹12,000 for 6 months. The total profit is ₹56,000. What is B's share?

BasicTry it yourself first

A starts a business with ₹6,000 and B joins after 3 months with ₹8,000. At the year’s end the profit is ₹34,500. What is B's share?

StandardTry it yourself first

A starts a business with ₹8,000 and B joins after 4 months with ₹12,000. At the year’s end the profit is ₹56,000. What is A's share?

AdvancedTry it yourself first

A starts a business with ₹12,500 and B joins after 6 months with ₹15,000. At the year’s end the profit is ₹47,600. What is B's share?

StandardTry it yourself first

A put in ₹5,000 for 12 months, B put in ₹6,000 for 8 months. B's share is ₹16,000. What is the total profit?

AdvancedTry it yourself first

A put in ₹8,000 for 12 months, B put in ₹10,000 for 9 months, C put in ₹6,000 for 6 months. A's share is ₹18,000. What is the total profit?

Changing capital and reversing the ratios

Count each stretch separately

Capital changes mid-year, or profit and capital ratios are given and the times are asked.

Capital changes: work out the capital-months of each stretch separately and add. Reversed ratios: profit $=$ capital × time, so time $= \frac{profit}{capital}$ — divide the profit ratio by the capital ratio.

Example 8 · Standard

Three partners’ capitals are in the ratio 2 : 3 : 5 and profits in the ratio 5 : 3 : 12. Find the ratio of times.

Solution, step by step

1Times $= \frac{5}{2} : \frac{3}{3} : \frac{12}{5}$ .
2Multiply by 10: $25 : 10 : 24$

Answer 25 : 10 : 24

Example 9 · Standard

A invests ₹8,000. B invests some amount 4 months later. At the year’s end the profit is split equally. How much did B invest?

Solution, step by step

1A: $8000 \times 12 = 96000$ . B: $x \times 8$ .
2Equal profit: $8 x = 96000$ ⟹ $x = 12000$

Answer ₹12,000

StandardTry it yourself first

A invests ₹5,000 and after 4 months changes the capital to ₹8,000. B keeps ₹6,000 for the whole year. The year’s profit is ₹39,000. What is A's share?

AdvancedTry it yourself first

A invests ₹10,000 and after 8 months changes the capital to ₹6,000. B keeps ₹9,000 for the whole year. The year’s profit is ₹47,700. What is A's share?

BasicTry it yourself first

Three partners’ capitals are in the ratio 3 : 2 : 4 and the profits in the ratio 1 : 1 : 1. What is the ratio of their investment times?

StandardTry it yourself first

Three partners’ capitals are in the ratio 4 : 5 : 6 and the profits in the ratio 12 : 10 : 15. What is the ratio of their investment times?

AdvancedTry it yourself first

Three partners’ capitals are in the ratio 5 : 7 : 9 and the profits in the ratio 45 : 35 : 63. What is the ratio of their investment times?

Working partners and rent

Salary first, then sharing

Profit after salary or commission, and sharing rent.

Working and sleeping partners

Take out the salary first

The working partner first gets a salary or commission; the balance goes by capital.

The active (working) partner runs the business and is paid a percentage (or fixed salary) first; the sleeping partner only invests. Method: (1) take out the salary / commission, (2) share the balance in the ratio of capital, (3) the working partner’s total = salary + his share.

Example 10 · Standard

A (working) and B (sleeping) put in ₹60,000 and ₹40,000. A gets 10% of the profit as salary and the rest goes by capital. Of a ₹50,000 profit how much does A get in all?

Solution, step by step

1Salary $= 5000$ ; split the balance $45000$ in $3 : 2$ : A $= 27000$ .
2A’s total $= 5000 + 27000 = 32000$

Answer ₹32,000

Example 11 · Standard

A and B start with ₹5,000 and ₹7,000; A manages and gets 5% of the profit. Of a ₹8,400 profit, what is A’s total?

Solution, step by step

1Commission $= 420$ ; split the balance $7980$ in $5 : 7$ : A $= 3325$ .
2A’s total $= 420 + 3325 = 3745$

Answer ₹3,745

BasicTry it yourself first

A (working partner) and B (sleeping partner) invest ₹30,000 and ₹20,000. A gets 10% of the profit as salary and the rest is shared in the ratio of capital. If the profit is ₹25,000, how much does A receive in all?

StandardTry it yourself first

A (working partner) and B (sleeping partner) invest ₹45,000 and ₹30,000. A gets 20% of the profit as salary and the rest is shared in the ratio of capital. If the profit is ₹60,000, how much does A receive in all?

AdvancedTry it yourself first

A (working partner) and B (sleeping partner) invest ₹36,000 and ₹24,000. A gets 12.5% of the profit as salary and the rest is shared in the ratio of capital. If the profit is ₹72,000, how much does A receive in all?

Sharing rent

Number × time

Rent of a pasture or godown — in the ratio of animals / goods × months.

The rent of a pasture or godown is shared just like a partnership — with the number of animals (or quantity of goods) in place of capital and months as the time. Take the ratio of each person’s “number × months”.

Example 12 · Standard

A pasture is rented for ₹4,140. A grazes 10 cows for 3 months, B 12 cows for 5 months and C 8 cows for 6 months. How much does B pay?

Solution, step by step

1Animal-months: $30, 60, 48$ (total 138).
2B pays $4140 \times \frac{60}{138} = 1800$

Answer ₹1,800

BasicTry it yourself first

A pasture is rented for ₹3,640. A grazed 10 animals for 4 months, B grazed 15 animals for 6 months. How much rent does B pay?

StandardTry it yourself first

A pasture is rented for ₹5,290. A grazed 8 animals for 6 months, B grazed 12 animals for 5 months, C grazed 10 animals for 3 months. How much rent does A pay?

AdvancedTry it yourself first

A pasture is rented for ₹8,080. A grazed 15 animals for 4 months, B grazed 12 animals for 6 months, C grazed 10 animals for 7 months. How much rent does C pay?

Traps and fast tricks

Slips · tricks

Where marks go in partnership.

The commonest mistakes

Six traps

The slips that cost marks.

Trap 1Forgetting time. The capital ratio is right only when everyone’s time is equal.

Trap 2Wrong time for a late joiner. “Joined after 3 months” means

12 - 3 = 9

months, not 3.

Trap 3Counting the salary again in the split. Take out the salary first, then share the balance.

Trap 4Splitting equally. Capitals of ₹40,000 and ₹60,000 give shares of 40% and 60%, not halves.

Trap 5Using one capital for the whole year when it changes. Add the capital-months of each stretch.

Trap 6Multiplying when finding time from the profit ratio. To get time divide profit by capital.

Fast tricks

Simplest ratio

Habits that shorten the work.

List the capital-months, then divide by their HCF — a small ratio is easier to work with.
A late joiner’s time: $12 - m$ .
Total profit ÷ total parts = one part; then each share = parts × one part.
If one share is known, find one part from it and then the total.
Capital and time are inverse: if two partners’ profits are equal, the capital ratio is the reverse of the time ratio.

Example 13 · Standard

A and B earn equal profits. A’s capital is ₹6,000 for 8 months; B stays 12 months. What is B’s capital?

Solution, step by step

1 $6000 \times 8 = C_{B} \times 12$ .
2 $C_{B} = \frac{48000}{12} = 4000$

Answer ₹4,000

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

A invested ₹2,000, B invested ₹3,000 in a partnership and after 1 year the profit was ₹15,000. What is B's share?

BasicTry it yourself first

A invested ₹5,000, B invested ₹7,000 in a partnership and after 1 year the profit was ₹24,000. What is A's share?

BasicTry it yourself first

A invested ₹1,000, B invested ₹2,000, C invested ₹3,000 in a partnership and after 1 year the profit was ₹18,000. What is C's share?

BasicTry it yourself first

2 partners each put in ₹10,000 and stayed 2, 4 months respectively. The total profit is ₹18,000. What is B's share?

BasicTry it yourself first

3 partners each put in ₹15,000 and stayed 3, 3, 6 months respectively. The total profit is ₹24,000. What is C's share?

BasicTry it yourself first

A put in ₹3,000 for 4 months, B put in ₹5,000 for 6 months. The total profit is ₹21,000. What is B's share?

BasicTry it yourself first

A put in ₹2,000 for 12 months, B put in ₹4,000 for 6 months. The total profit is ₹30,000. What is A's share?

BasicTry it yourself first

A starts a business with ₹4,000 and B joins after 6 months with ₹6,000. At the year’s end the profit is ₹21,000. What is A's share?

BasicTry it yourself first

A put in ₹3,000, B put in ₹7,000. The business lost ₹8,000. What is A's share of the loss?

BasicTry it yourself first

A put in ₹4,000, B put in ₹6,000, C put in ₹10,000. The business lost ₹10,000. What is C's share of the loss?

BasicTry it yourself first

A invests ₹4,000 and after 6 months changes the capital to ₹6,000. B keeps ₹5,000 for the whole year. The year’s profit is ₹20,000. What is A's share?

BasicTry it yourself first

A (working partner) and B (sleeping partner) invest ₹20,000 and ₹20,000. A gets 20% of the profit as salary and the rest is shared in the ratio of capital. If the profit is ₹10,000, how much does A receive in all?

BasicTry it yourself first

Three partners’ capitals are in the ratio 2 : 3 : 4 and the profits in the ratio 3 : 3 : 2. What is the ratio of their investment times?

BasicTry it yourself first

A pasture is rented for ₹4,800. A grazed 6 animals for 4 months, B grazed 8 animals for 3 months. How much rent does A pay?

BasicTry it yourself first

A put in ₹3,000 for 12 months, B put in ₹4,000 for 6 months. A's share is ₹3,900. What is the total profit?

BasicTry it yourself first

A invested ₹3,000, B invested ₹5,000 in a partnership and after 1 year the profit was ₹16,000. What is A's share?

BasicTry it yourself first

A invested ₹2,500, B invested ₹7,500 in a partnership and after 1 year the profit was ₹20,000. What is B's share?

BasicTry it yourself first

2 partners each put in ₹12,000 and stayed 1, 3 months respectively. The total profit is ₹16,000. What is A's share?

BasicTry it yourself first

2 partners each put in ₹8,000 and stayed 4, 8 months respectively. The total profit is ₹18,000. What is B's share?

BasicTry it yourself first

A put in ₹2,000 for 6 months, B put in ₹3,000 for 4 months. The total profit is ₹18,000. What is B's share?

BasicTry it yourself first

A put in ₹1,000 for 12 months, B put in ₹4,000 for 3 months. The total profit is ₹20,000. What is A's share?

BasicTry it yourself first

A starts a business with ₹2,000 and B joins after 6 months with ₹4,000. At the year’s end the profit is ₹20,000. What is B's share?

BasicTry it yourself first

A put in ₹5,000, B put in ₹15,000. The business lost ₹12,000. What is B's share of the loss?

BasicTry it yourself first

A (working partner) and B (sleeping partner) invest ₹10,000 and ₹30,000. A gets 10% of the profit as salary and the rest is shared in the ratio of capital. If the profit is ₹20,000, how much does A receive in all?

BasicTry it yourself first

A pasture is rented for ₹3,000. A grazed 5 animals for 6 months, B grazed 10 animals for 3 months. How much rent does B pay?

BasicTry it yourself first

A put in ₹2,000 for 12 months, B put in ₹3,000 for 8 months. A's share is ₹6,000. What is the total profit?

Level 2 — Standard

Two ideas combined

Exam-level questions.

StandardTry it yourself first

A invested ₹14,000, B invested ₹21,000, C invested ₹35,000 in a partnership and after 1 year the profit was ₹70,000. What is B's share?

StandardTry it yourself first

A invested ₹12,000, B invested ₹18,000, C invested ₹30,000 in a partnership and after 1 year the profit was ₹45,000. What is C's share?

StandardTry it yourself first

3 partners each put in ₹25,000 and stayed 5, 8, 11 months respectively. The total profit is ₹72,000. What is B's share?

StandardTry it yourself first

3 partners each put in ₹36,000 and stayed 4, 6, 10 months respectively. The total profit is ₹40,000. What is C's share?

StandardTry it yourself first

A put in ₹8,000 for 12 months, B put in ₹6,000 for 10 months, C put in ₹4,000 for 9 months. The total profit is ₹66,000. What is B's share?

StandardTry it yourself first

A put in ₹7,500 for 8 months, B put in ₹9,000 for 6 months. The total profit is ₹51,300. What is A's share?

StandardTry it yourself first

A put in ₹10,000 for 12 months, B put in ₹12,000 for 8 months, C put in ₹15,000 for 4 months. The total profit is ₹78,200. What is C's share?

StandardTry it yourself first

A starts a business with ₹9,000 and B joins after 3 months with ₹12,000. At the year’s end the profit is ₹64,500. What is B's share?

StandardTry it yourself first

A starts a business with ₹15,000 and B joins after 5 months with ₹20,000. At the year’s end the profit is ₹82,400. What is A's share?

StandardTry it yourself first

A put in ₹18,000, B put in ₹27,000, C put in ₹45,000. The business lost ₹36,000. What is B's share of the loss?

StandardTry it yourself first

A invests ₹6,000 and after 5 months changes the capital to ₹9,000. B keeps ₹7,000 for the whole year. The year’s profit is ₹70,800. What is A's share?

StandardTry it yourself first

A (working partner) and B (sleeping partner) invest ₹40,000 and ₹60,000. A gets 12% of the profit as salary and the rest is shared in the ratio of capital. If the profit is ₹55,000, how much does A receive in all?

StandardTry it yourself first

A (working partner) and B (sleeping partner) invest ₹50,000 and ₹30,000. A gets 25% of the profit as salary and the rest is shared in the ratio of capital. If the profit is ₹64,000, how much does A receive in all?

StandardTry it yourself first

Three partners’ capitals are in the ratio 3 : 4 : 5 and the profits in the ratio 15 : 12 : 20. What is the ratio of their investment times?

StandardTry it yourself first

Three partners’ capitals are in the ratio 5 : 6 : 8 and the profits in the ratio 15 : 24 : 20. What is the ratio of their investment times?

StandardTry it yourself first

A pasture is rented for ₹8,680. A grazed 12 animals for 5 months, B grazed 9 animals for 4 months, C grazed 15 animals for 6 months. How much rent does C pay?

StandardTry it yourself first

A pasture is rented for ₹7,310. A grazed 8 animals for 6 months, B grazed 10 animals for 3 months, C grazed 6 animals for 4 months. How much rent does A pay?

StandardTry it yourself first

A put in ₹6,000 for 12 months, B put in ₹9,000 for 8 months. B's share is ₹18,000. What is the total profit?

StandardTry it yourself first

A put in ₹4,000 for 12 months, B put in ₹5,000 for 6 months, C put in ₹6,000 for 9 months. C's share is ₹16,200. What is the total profit?

StandardTry it yourself first

A invested ₹16,000, B invested ₹24,000, C invested ₹40,000 in a partnership and after 1 year the profit was ₹80,000. What is C's share?

StandardTry it yourself first

A invested ₹11,000, B invested ₹22,000, C invested ₹33,000 in a partnership and after 1 year the profit was ₹66,000. What is A's share?

StandardTry it yourself first

3 partners each put in ₹20,000 and stayed 3, 7, 12 months respectively. The total profit is ₹66,000. What is B's share?

StandardTry it yourself first

3 partners each put in ₹28,000 and stayed 5, 6, 10 months respectively. The total profit is ₹63,000. What is A's share?

StandardTry it yourself first

A put in ₹9,000 for 8 months, B put in ₹12,000 for 6 months, C put in ₹6,000 for 12 months. The total profit is ₹54,000. What is C's share?

StandardTry it yourself first

A put in ₹5,400 for 10 months, B put in ₹7,200 for 15 months. The total profit is ₹39,900. What is B's share?

StandardTry it yourself first

A starts a business with ₹7,500 and B joins after 8 months with ₹15,000. At the year’s end the profit is ₹45,000. What is A's share?

StandardTry it yourself first

A starts a business with ₹18,000 and B joins after 6 months with ₹24,000. At the year’s end the profit is ₹60,000. What is B's share?

StandardTry it yourself first

A put in ₹12,000, B put in ₹20,000, C put in ₹28,000. The business lost ₹24,000. What is A's share of the loss?

StandardTry it yourself first

A invests ₹8,000 and after 6 months changes the capital to ₹12,000. B keeps ₹9,000 for the whole year. The year’s profit is ₹60,800. What is A's share?

StandardTry it yourself first

A (working partner) and B (sleeping partner) invest ₹35,000 and ₹45,000. A gets 15% of the profit as salary and the rest is shared in the ratio of capital. If the profit is ₹48,000, how much does A receive in all?

StandardTry it yourself first

A pasture is rented for ₹8,580. A grazed 7 animals for 6 months, B grazed 14 animals for 4 months, C grazed 9 animals for 5 months. How much rent does B pay?

StandardTry it yourself first

A put in ₹7,000 for 12 months, B put in ₹8,000 for 9 months. B's share is ₹21,000. What is the total profit?

Level 3 — Advanced

Many steps and clever thinking

Questions at the hard end of competitive exams.

AdvancedTry it yourself first

A invested ₹18,000, B invested ₹24,000, C invested ₹30,000, D invested ₹48,000 in a partnership and after 1 year the profit was ₹96,000. What is D's share?

AdvancedTry it yourself first

3 partners each put in ₹48,000 and stayed 5, 9, 13 months respectively. The total profit is ₹1,08,000. What is C's share?

AdvancedTry it yourself first

A put in ₹16,000 for 9 months, B put in ₹12,000 for 12 months, C put in ₹20,000 for 6 months. The total profit is ₹1,03,700. What is B's share?

AdvancedTry it yourself first

A put in ₹8,500 for 12 months, B put in ₹11,000 for 6 months, C put in ₹6,000 for 10 months. The total profit is ₹85,500. What is A's share?

AdvancedTry it yourself first

A starts a business with ₹24,000 and B joins after 4 months with ₹30,000. At the year’s end the profit is ₹88,000. What is B's share?

AdvancedTry it yourself first

A starts a business with ₹32,000 and B joins after 7 months with ₹48,000. At the year’s end the profit is ₹1,56,000. What is A's share?

AdvancedTry it yourself first

A put in ₹32,000, B put in ₹40,000, C put in ₹56,000, D put in ₹72,000. The business lost ₹40,000. What is D's share of the loss?

AdvancedTry it yourself first

A invests ₹12,000 and after 7 months changes the capital to ₹8,000. B keeps ₹10,000 for the whole year. The year’s profit is ₹1,22,000. What is A's share?

AdvancedTry it yourself first

A (working partner) and B (sleeping partner) invest ₹75,000 and ₹45,000. A gets 15% of the profit as salary and the rest is shared in the ratio of capital. If the profit is ₹96,000, how much does A receive in all?

AdvancedTry it yourself first

A (working partner) and B (sleeping partner) invest ₹54,000 and ₹36,000. A gets 8% of the profit as salary and the rest is shared in the ratio of capital. If the profit is ₹1,25,000, how much does A receive in all?

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Three partners’ capitals are in the ratio 7 : 8 : 9 and the profits in the ratio 56 : 72 : 63. What is the ratio of their investment times?

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Three partners’ capitals are in the ratio 4 : 9 : 11 and the profits in the ratio 36 : 99 : 44. What is the ratio of their investment times?

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A pasture is rented for ₹17,270. A grazed 18 animals for 5 months, B grazed 15 animals for 7 months, C grazed 20 animals for 4 months. How much rent does B pay?

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A pasture is rented for ₹22,200. A grazed 24 animals for 6 months, B grazed 18 animals for 8 months, C grazed 16 animals for 9 months. How much rent does C pay?

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A put in ₹9,000 for 12 months, B put in ₹12,000 for 9 months, C put in ₹15,000 for 8 months. B's share is ₹27,000. What is the total profit?

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A put in ₹7,000 for 12 months, B put in ₹8,000 for 9 months. A's share is ₹21,000. What is the total profit?

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A invested ₹21,000, B invested ₹28,000, C invested ₹35,000, D invested ₹56,000 in a partnership and after 1 year the profit was ₹1,00,000. What is B's share?

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3 partners each put in ₹54,000 and stayed 4, 6, 11 months respectively. The total profit is ₹1,05,000. What is C's share?

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A put in ₹11,000 for 12 months, B put in ₹14,000 for 7 months, C put in ₹9,000 for 10 months. The total profit is ₹98,000. What is A's share?

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A put in ₹6,500 for 9 months, B put in ₹8,000 for 12 months, C put in ₹9,500 for 8 months. The total profit is ₹92,200. What is C's share?

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A starts a business with ₹27,000 and B joins after 5 months with ₹36,000. At the year’s end the profit is ₹96,000. What is A's share?

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A starts a business with ₹42,000 and B joins after 9 months with ₹54,000. At the year’s end the profit is ₹1,11,000. What is B's share?

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A put in ₹15,000, B put in ₹22,500, C put in ₹37,500. The business lost ₹30,000. What is B's share of the loss?

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A invests ₹15,000 and after 4 months changes the capital to ₹10,000. B keeps ₹12,000 for the whole year. The year’s profit is ₹1,49,100. What is A's share?

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A (working partner) and B (sleeping partner) invest ₹66,000 and ₹44,000. A gets 20% of the profit as salary and the rest is shared in the ratio of capital. If the profit is ₹1,20,000, how much does A receive in all?

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Three partners’ capitals are in the ratio 6 : 8 : 9 and the profits in the ratio 8 : 12 : 9. What is the ratio of their investment times?

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A pasture is rented for ₹12,070. A grazed 16 animals for 5 months, B grazed 24 animals for 4 months, C grazed 12 animals for 8 months. How much rent does A pay?

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A put in ₹10,000 for 12 months, B put in ₹12,000 for 6 months, C put in ₹8,000 for 9 months. C's share is ₹15,900. What is the total profit?

Revision — formula cards

Flip each card and test yourself

Read the front, think, then flip.