In this article we have solved the questions previously asked in SSC CGL Mains/Tier II. If at any stage you find difficulty in understanding the solution, you may refer our concept post on Partnership – Concepts, Types and Solved Problems.

## SSC CGL MAINS 2020

**Q1**. A, B and C invested their capitals in the ratio 2 : 3 : 5. The ratio of months for which they invested is 4 : 2 : 3 respectively. If the difference between the profit shares of A and B is ₹1,86,000 then C’s share of profit (in ₹) is:

(a) 15,39,000

(b) 19,35,000

(c) 13,95,000

(d) 10,29,000

{Held on: Jan 29, 2022}

**Ans:** (c) 13,95,000

**Explanation:**

A : B : C

I⟶ 2 : 3 : 5

T⟶ 4 : 2 : 3

______________________________

P⟶ 8 : 6 : 15

A – B = 8 – 6 = 2 part

2 part = 186000

⇒ 15 part = 930000 × 15

= 1395000

**Q2**. A started a business with a capital of ₹54,000 and admitted B and C after 4 months and 6 months respectively. At the end of the year, the profit was divided among the three in the ratio 1 : 4 : 5. What is the sum (in ₹) of the capitals invested by B and C?

(a) 8,60,400

(b) 8,40,060

(c) 8,46,000

(d) 8,64,000

{Held on: Jan 29, 2022}

**Ans:** (d) 8,64,000

**Explanation:**

A : B : C

I⟶

T⟶ 12 : 8 : 6 = 6 : 4 : 3

______________________________

P⟶ 1 : 4 : 5

\text{P} = \text{IT} ⇒ \text{I} = \displaystyle \frac{\text{P}}{\text{T}}

I ⟶ \displaystyle \frac{1}{6} : \displaystyle \frac{4}{4} : \displaystyle \frac{5}{3} = \displaystyle \frac{1}{6} : 1 : \displaystyle \frac{5}{3} = 1:6:10

1 part = 54000

⇒16 part = 864000

**Q3**. P and Q start a shop with a capital of ₹1,50,000 and 4,50,000 respectively. After a year, out of the profit of ₹2,00,000, P gets his share of profit plus some money as his salary that is not a part of the profit. If P gets a total of ₹90,000, what is the amount of salary (in ₹) that he received?

(a) 20,000

(b) 25,000

(c) 50,000

(d) 40,000

{Held on: Feb 3, 2022}

**Ans:** (d) 40,000

**Explanation**:

Investment ratio of P and Q = 150000 : 450000 = 1 : 3

P’s share in profit = \displaystyle\frac{1}{4}\times 200000 = 50000

But P get 90000

So, salary of C = 90000 – 50000 = 40000

**Q4**. The ratio of the investments of A and B in a business is 7 : 5, and the ratio of their profits at the end of a year is 2 : 5. If A invested the money for 6 months, then for how much time (in months) has B invested his money?

(a) 24

(b) 21

(c) 20

(d) 18

{Held on: Feb 3, 2022}

**Ans**: (b) 21

**Explanation**:

A : B

I⟶ 7 : 5

T⟶ \displaystyle\frac{2}{7} : 1 = 2 : 7

______________________________

P⟶ 2 : 5

## SSC CGL MAINS 2019

**Q1**. A, B and C started a business. Twice the investment of A is equal to thrice the investment of B and also five times the investment of C. If the total profit after a year is ₹15.5 lakhs, then the share of B in the profit is (in ₹ lakhs):

(a) 7.5

(b) 3

(c) 5

(d) 4.5

{Held on: Nov 15, 2020}

**Ans**: (c) 5

**Explanation**:

2A = 3B = 5C

A : B : C = \displaystyle\frac{1}{2} : \displaystyle\frac{1}{3} : \displaystyle\frac{1}{5} = 15 : 10 : 6

B’s share = \displaystyle\frac{10}{31}\times 15.5 = 5

**Q2**. X and Y enter into a partnership with capital in the ratio 3 : 5. After 5 months X adds 50% of his capital, while Y withdraws 60% of his capital. What is the share (in ₹ lakhs) of X in the annual profit of ₹6.84 lakhs?

(a) 3.72

(b) 4.2

(c) 3.6

(d) 3.12

{Held on: Nov 15, 2020}

**Ans**: (a) 3.72

**Explanation**:

X : Y

IT⟶ 3×5 : 5×5

IT⟶ 4.5×7 : 2×7

______________________________

P⟶ 15+31.5 : 25+14

= 46.5 : 39

= 465 : 390

= 31 : 26

X’s share = \displaystyle\frac{31}{57}\times 6.84 = 3.72

**Q3**. A and B enter into a partnership with capital in the ratio 5 : 6. After 4 months, A withdraws \displaystyle\frac{1}{5}th of his capital, while B increases his capital by 33\displaystyle \frac{1}{3}\%. What is the share (in ₹ lakhs) of B in the annual profit of ₹6.3 lakhs?

(a) 2.34

(b) 2.61

(c) 3.69

(d) 3.96

{Held on: Nov 16, 2020}

**Ans**: (d) 3.96

**Explanation**:

A : B

IT⟶ 5×4 : 6×4

IT⟶ 4×8 : 8×8

______________________________

P⟶ 20+32 : 24+64

= 52 : 88

= 13 : 22

B’s share = \displaystyle\frac{22}{35}\times 6.3 = 3.96

**Q4**. A, B and C invested capital in the ratio 5 : 7 : 4, the timing of their investments being in the ratio x : y : z. If their profits are distributed in the ratio 45 : 42 : 28, then x : y : z = ?

(a) 9 : 6 : 7

(b) 6 : 7 : 9

(c) 9 : 4 : 7

(d) 7 : 9 : 4

{Held on: Nov 16, 2020}

**Ans**: (a) 9 : 6 : 7

**Explanation**:

A : B : C

I⟶ 5 : 7 : 4

T⟶ 9 : 6 : 7

______________________________

P⟶ 45 : 42 : 28

T we have got as \text{P} = \text{IT} ⇒ \text{T} = \displaystyle \frac{\text{P}}{\text{I}}

Hence, x : y : z = 9 : 6 : 7

**Q5.** A, B and C together invests ₹53,000 in a business. A invests ₹5,000 more than B and B invests ₹6,000 more than C. Out of a total profit of ₹31,800, find the share of A.

(a) ₹13,800

(b) ₹12,800

(c) ₹12,500

(d) ₹13,500

{Held on: Nov 18, 2020}

**Ans**: (a) ₹13,800

**Explanation**:

C = x

B = x + 6000

A = x + 6000 + 5000 = x + 11000

Now, A + B + C = 53000

∴ 3x + 17000 = 530000

⇒ 3x = 36000

⇒ x = 12000

A’s capital = x + 11000 = 12000 + 11000 = 23000

A’s share = \displaystyle\frac{23000}{53000}\times 31800 = 13800

**Q6.** Ramesh started a business investing a sum of ₹40,000. Six months later, Kevin joined by investing ₹20,000. If they make a profit of ₹10,000 at the end of the year, how much is the share of Kevin?

(a) ₹3,000

(b) ₹4,000

(c) ₹2,500

(d) ₹2,000

{Held on: Nov 18, 2020}

**Ans**: (d) ₹2,000

**Explanation**:

R : K

I⟶ 40000 : 20000 = 2 : 1

T⟶ 12 : 6 = 2 : 1

______________________________

P⟶ 4 : 1

Kevin’s share = \displaystyle\frac{1}{5}\times 10000 = 2000

## SSC CGL MAINS 2018

**Q1.** A started a business with a capital of ₹54,000 and admitted B and C after 4 months and 6 months, respectively. At the end of the year, the profit was divided in the ratio 1 : 4 : 5. What is the difference between the capitals invested by B and C?

(a) 216000

(b) 324000

(c) 108000

(d) 162000

{Held on: Sept. 11, 2019}

**Ans**: (a) 216000

**Explanation**:

A : B : C

I⟶ \displaystyle\frac{1}{6} : \displaystyle\frac{4}{4} : \displaystyle\frac{5}{3} = 1 : 6 :10

T⟶ 12 : 8 : 6 = 6 : 4 : 3

______________________________

P⟶ 1 : 4 : 5

∴ investment ratio by A, B and C = 1 : 6 : 10

Difference between B and C = 10 – 6 = 4

Now, 1 part = 54000

⇒ 4 part = 216000

**Q2.** The ratio of investment by A to that by B in a business is 14 : 15 and the ratio of their respective profits at the end of a year is 2 : 5. If A invested the money for 3 months, then for how much time (in months) B invested his money?

(a) 6

(b) 9

(c) 5

(d) 7

{Held on: Sept. 11, 2019}

**Ans**: (d) 7

**Explanation**:

A : B

I⟶ 14 : 15

T⟶ \displaystyle\frac{1}{7} : \displaystyle\frac{1}{3} = 3 : 7

______________________________

P⟶ 2 : 5

3 part = 3 months

⇒ 4 part = 7 months

**Q3.** A, B and C start a business. A invests 33\displaystyle\frac{1}{3}\% of the total capital, B invests 25% of the remaining and C invests the rest. If the total profit at the end of a year is ₹162,000, then A’s share in the profit is:

(a) ₹81000

(b) ₹60000

(c) ₹54000

(d) ₹90000

{Held on: Sept. 12, 2019}

**Ans**: (c) ₹54000

**Explanation**:

33\displaystyle\frac{1}{3}\% = \displaystyle\frac{1}{3}

Let, total profit = 3 part

∴ A’s capital = 1

B’s capital = 0.5

C’s capital = 1.5

A : B : C = 1 : 0.5 : 1.5 = 2 : 1 : 3

A’s share of profit = \displaystyle\frac{2}{6}\times 162000 = 54000

**Aliter:**

See A’s capital is 33\displaystyle\frac{1}{3}\% = \displaystyle\frac{1}{3}rd of capital

So, profit will also be \displaystyle\frac{1}{3}rd of profit

Hence, A’s share = \displaystyle\frac{1}{3}\times 162000 = 54000

If B’s or C’s share was asked in that case finding B’s part or C’s part was necessary which we have done earlier.

**Q4.** A, B and C invested their capitals in the ratio of 2 : 3 : 5. The ratio of months for which A, B and C invested is 4 : 2 : 3. If C gets a share of profit which is ₹147,000 more than that of A, then B’s share of profit is:

(a) 126,000

(b) 168,000

(c) 105,000

(d) 189,000

{Held on: Sept. 12, 2019}

**Ans:** (a) 126,000

**Explanation**:

A : B : C

I⟶ 2 : 3 : 5

T⟶ 4 : 2 : 3

______________________________

P⟶ 8 : 6 : 15

C – A = 15 – 8 = 7 part

7 part = 147000

⇒ 6 part = 21000 × 6

= 126000

**Q5.** A, B and C started a business with their capitals in the ratio 2 : 3 : 5. A increased his capitals by 50% after 4 months, B increased his capitals by 33\displaystyle\frac{1}{3}\% after 6 months and C withdrew 50% of his capital after 8 months, from the start of the business. If the total profit at the end of year was ₹86,800, then the difference between the shares of A and C in the profit was:

(a) ₹12,600

(b) ₹7,000

(c) ₹9,800

(d) ₹8,400

{Held on: Sept. 13, 2019}

**Ans:** (a) ₹12,600

**Explanation:**

A : B : C

IT⟶ 2×4 : 3×6 : 5×8

IT⟶ 3×8 : 4×6 : 2.5×4

______________________________

P⟶ 8 + 24 : 18 + 24 : 40 + 10

= 32 : 42 : 50

= 16 : 21 : 25

62 part = 86800

⇒ 9 part = \displaystyle\frac{86800\times 9}{62} = 12600

**Q6.** A, B and C started a business. Thrice the investment of A is equal to twice the investment of B and also equal to four times the investment of C. If C’s share out of the total profit is ₹4863, then the share of A in the profit is:

(a) 7,272

(b) 6,484

(c) 9,726

(d) 8,105

{Held on: Sept. 13, 2019}

**Ans**: (b) 6,484

3A = 2B = 4C

A : B : C = \displaystyle\frac{1}{3} : \displaystyle\frac{1}{2} : \displaystyle\frac{1}{4} = 8 : 12 : 6 = 4 : 6 : 3

3 part = 4863

⇒ 4 part = 1621 × 4

= 6484

## SSC CGL MAINS 2017

**Q1**. A and B started a partnership business investing in the ratio of 3 : 8. C joined them after 4 months with an amount equal to \displaystyle\frac{3}{4}th of B. What was their profit (in ₹) at the end of the year if C got ₹24,000 as his share?

(a) 120000

(b) 150000

(c) 90000

(d) 180000

{Held on: Feb 17, 2018}

**Ans**: (c) 90000

**Explanation**:

A : B : C

I⟶ 3 : 8 : 6 = 3 : 8 : 6

T⟶ 12 : 12 : 8 = 3 : 3 : 2

______________________________

P⟶ 9 : 24 : 12

= 3 : 8 : 4

4 part = 24000

⇒ 15 part = 90000

**Q2**. A and B invest in a business in the ratio 4 : 5. After 10 months B leaves the business after withdrawing his investment. In the first year the business made a profit of ₹49,000. What is B’s share (in ₹) of this profit?

(a) 25000

(b) 20000

(c) 18000

(d) 22000

{Held on: Feb 17, 2018}

**Ans**: (a) 25000

**Explanation**:

A : B

I⟶ 4 : 5 = 4 : 5

T⟶ 12 : 10 = 6 : 5

______________________________

P⟶ 24 : 25

B’s share = \displaystyle\frac{25}{49}\times 490000= 25000

**Q3. **A starts a taxi service by investing ₹25 lakhs. After 3 months, B joins the business by investing ₹40 lakhs then 4 months after B joined, C too joins them by investing ₹50 lakhs. One year after A started the business they make ₹2,73,000 in profit. What is C’s share of the profit (in ₹)?

(a) 100000

(b) 125000

(c) 75000

(d) 150000

{Held on: Feb 18, 2018}

**Ans**: (c) 75000

**Explanation**:

A : B : C

I⟶ 25 : 40 : 50 = 5 : 8 : 10

T⟶ 12 : 9 : 5 = 12 : 9 : 5

______________________________

P⟶ 60 : 72 : 50 = 30 : 36 : 25

C’s share = \displaystyle\frac{25}{91}\times 273000=75000

**Q4**. A, B and C invest in a business in the ratio 4 : 5 : 7. C is a sleeping partner, so his share of profits will be half of what it would have been if he were a working partner. If they make ₹36,000 profit of which 25% is reinvested in the business, how much does B get (in ₹)?

(a) 7560

(b) 10800

(c) 8640

(d) 9200

{Held on: Feb 18, 2018}

**Ans**: (b) 10800

**Explanation**:

Investment ratio of A, B and C = 4 : 5 : 7

C is a sleeping partner.

So, his part in the profit is \displaystyle \frac{7}{2}

Now, profit ratio = 4 : 5 : \displaystyle \frac{7}{2} = 8 : 10 : 7

25% of profit is reinvested in the business

So, profit distributed among them = 75% × 3600 = 2700

Hence B’s share = \displaystyle\frac{10}{25}\times 2700=10800

**Q5**. A and B started a partnership business investing some amount in the ratio of 5 : 6. C joined them after 6 months with an amount equal to \displaystyle\frac{2}{3} rd of B. What was their profit (in ₹) at the end of the year if C got ₹21,600 as his share?

(a) 46800

(b) 56160

(c) 70200

(d) 140400

{Held on: Feb 19, 2018}

**Ans**: (d) 140400

**Explanation**:

A : B : C

I⟶ 5 : 6 : 4 = 5 : 6 : 4

T⟶ 12 : 12 : 6 = 2 : 2 : 1

______________________________

P⟶ 10 : 12 : 4 = 5 : 6 : 2

2 part = 21600

⇒ 13 part = 10800 × 13

= 140400

**Q6**. A, B and C invest to start a restaurant. The total investment was ₹3 lakhs. B invested ₹50,000 more than A and C invested ₹25,000 less than B. If the profit at the end of the year was ₹14,400 then what is C’s share of the profit (in ₹)?

(a) 3600

(b) 4800

(c) 6000

(d) 7200

{Held on: Feb 20, 2018}

**Ans**: (b) 4800

**Explanation**:

Let, investment by A = x

Hence, investment by B = x + 50000

And investment by C = (x + 50000) – 25000 = x + 25000

Now, total investment = 3 lakhs = 300000

∴ x + x + 50000 + x + 25000 = 300000

⇒ 3x + 75000 = 300000

⇒ 3x = 225000

⇒ x = 75000

∴ Investment by C = x + 25000 = 75000 + 25000 = 100000

Now, C’s share = \displaystyle\frac{100000}{300000}\times 144000=4800

**Q7**. Two businessman A and B invest in a business in the ratio 5 : 8. They decided to reinvest 30% of the profit they earned back into the business. The remaining profit they distributed amongst themselves. If A’s share of the profit was ₹87,500 then how much profit (in ₹) did the business make?

(a) 227000

(b) 250000

(c) 375000

(d) 325000

{Held on: Feb 20, 2018}

**Ans:** (d) 325000

**Explanation:**

A : B = 5 : 8

A’s profit = 87500

∴ 5 part = 87500

⇒ 13 part = 17500 × 13 = 70% of profit

∴ 100% = \displaystyle\frac{17500\times 13}{70}\times 100=325000

## SSC CGL MAINS 2016

**Q1**. A, B and C together start a business. Three times the investment of A equals four times the investment of B and the capital of B is twice that of C. The ratio of share of each in the profit

(a) 8 : 3 : 6

(b) 3 : 8 : 6

(c) 3 : 6 : 8

(d) 8 : 6 : 3

{Held on : Nov 30, 2016}

**Ans**: (d) 8 : 6 : 3

**Explanation**:

3A = 4B and B = 2C

⇒ A : B = 4 : 3 and B: C = 2 : 1

∴ A : B : C = 8 : 6 : 3

**Q2**. A and B start an enterprise together , with A as active partner. A invests ₹4000 and ₹2000 more after 8 months. B invests ₹5000 and withdraws ₹2000 after 9 months. Being the active partner, A takes ₹100 per month as allowance, from the profit. What is the share of B if the profit for the year is ₹6700?

(a) ₹3350

(b) ₹3250

(c) ₹2700

(d) ₹2800

{Held on: Jan 12, 2017}

**Ans**: (c) ₹2700

**Explanation**:

A : B

IT⟶ 4000×8 : 5000×9

IT⟶ 6000×4 : 3000×3

______________________________

P⟶ 32000+2400 : 4500+9000

= 5600 : 5400

= 28 : 27

A is active partner.

Allowance withdrawn by A = 100 × 12 = 1200

Rest profit = 6700 – 1200 = 5500

B’s share = \displaystyle \frac{27}{55}\times 5500 = 2700

## SSC CGL MAINS 2014

**Q1**. In a partnership business, B’s capital was half of A’s. After 8 months, B withdrew half of his capital and and after 2 months more A withdrew \displaystyle \frac{1}{4}th of his capital, the the, profit ratio of A and B will be

(a) 10 : 23

(b) 23 : 10

(c) 5 : 2

(d) 2 : 5

{Held on: Apr 12, 2015}

**Ans**: (b) 23 : 10

**Explanation**:

Let, capital of A = 4.

A : B

IT⟶ 4×10 : 2×8

IT⟶ 3×2 : 1×4

______________________________

P⟶ 40+6 : 16+4

= 46 : 20

= 23 : 10

**Q2**. A and B invest in the ratio 3 : 5. After 6 months , C joins the business, investing an amount equal to B’s. At the end of the year what will be the ratio of their profits?

(a) 3 : 5 : 2

(b) 1 : 5 : 5

(c) 6 : 10 : 5

(d) 8 : 10 : 5

{Held on: Apr 12, 2015}

**Ans**: (c) 6 : 10 : 5

**Explanation**:

A : B : C

I⟶ 3 : 5 : 5 = 3 : 5 : 5

T⟶ 12 : 12 : 6 = 2 : 2 : 1

______________________________

P⟶ 6 : 10 : 5

## SSC CGL MAINS 2012

Q1. A and B started a business with ₹20,000 and ₹35,000 respectively. The agreed to share the profit in the ratio of their capital. C joins the partnership with the condition that A, B, C will share profit equally and pays 2,20,000 as the premium for this, to be shared between A and B. This to divided between A and B in the ratio of

(a) 9 : 10

(b) 10 : 9

(c) 10 : 1

(d) 1 : 10

{Held on: Sep 16, 2012}

**Ans**: (d) 1 : 10

**Explanation**:

Initial investment ratio of A and B

= 20000 : 35000

= 4 : 7

A’s share = \displaystyle\frac{4}{11}

B’s share = \displaystyle\frac{7}{11}

Now, C joins the partnership with the condition that total profit must be equally divided among A, B and C.

So, ratio should be 1 : 1 : 1

Now, A’s share = \displaystyle\frac{1}{3}

B’s share = \displaystyle\frac{1}{3}

Decrease in profit of A = \displaystyle\frac{4}{11} - \displaystyle\frac{1}{3} = \displaystyle\frac{1}{33}

Decrease in profit of B = \displaystyle\frac{7}{11} - \displaystyle\frac{1}{3} = \displaystyle\frac{10}{33}

So, premium will be divided in decreased profit ratio = \displaystyle\frac{1}{33} : \displaystyle\frac{10}{33} = 1 : 10

**Extra**:

A will get premium = \displaystyle\frac{1}{11}\times 220000 = 20000

B will get premium = \displaystyle\frac{10}{11}\times 220000 = 200000

## SSC CGL MAINS 2010

Q1. A and B enter into partnership with capitals in the ratio 5 : 6. At the end of 8 months A withdraws his capital. They received profits in the ratio 5 : 9. B invested the capital for

(a) 6 months

(b) 8 months

(c) 10 months

(d) 12 months

{Held on: Aug 1, 2010}

**Ans**: (d) 12 months

**Explanation**:

Ratios are as A : B

I ⟶ 5 : 6

T ⟶

____________________

P ⟶ 5 : 9

Now, T ⟶ \displaystyle \frac{5}{5}:\displaystyle \frac{9}{6} = 1 :\displaystyle \frac{3}{2} = 2 : 3

2 part = 8 months

3 part = 12 months

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