# CRE 4 - Partnership | Arithmetic - Ratio, Proportion & Variation

**CRE 4 - Partnership | Arithmetic - Ratio, Proportion & Variation**

Ankush and Vishal started a business by investing Rs. 3000 and Rs. 5000 respectively. At the end of the year they earned a profit of Rs. 1600. Find the share of Vishal in the total profit.

- (a)
Rs. 600

- (b)
Rs. 1200

- (c)
Rs. 800

- (d)
Rs. 1000

Answer: Option D

**Explanation** :

Since both of them invest for the same amount of time, profit will be divided in the ratio of their investments.

Ratio of investment for Ankush and Vishal = 3000 : 5000 = 3 : 5

Hence, share of Vishal = 5/8 × 1600 = 1000.

Hence, option (d).

Workspace:

**CRE 4 - Partnership | Arithmetic - Ratio, Proportion & Variation**

Ankush and Vishal started a business by investing Rs. 3000 each. Ankush left the business after 7 months and withdrew his entire investment while Vishal stayed in the business till the end. At the end of the year they earned a profit of Rs. 3800. Find the share of Ankush in the total profit.

- (a)
Rs. 1200

- (b)
Rs. 1400

- (c)
Rs. 2400

- (d)
Rs. 2000

Answer: Option B

**Explanation** :

Since both of them invested the same amount, profit will be divided in the ratio of their time they were invested for.

Ratio of investment for Ankush and Vishal = 7 months : 12 months = 7 : 12

Hence, share of Ankush = 7/19 × 3800 = 1400.

Hence, option (b).

Workspace:

**CRE 4 - Partnership | Arithmetic - Ratio, Proportion & Variation**

Ankush and Vishal started a business by investing Rs. 3000 and Rs. 5000 respectively. Ankush left the business after 7 months and withdrew his entire investment while Vishal stayed in the business till the end. At the end of the year they earned a profit of Rs. 5400. Find the difference between the profit received by the two.

- (a)
Rs. 1200

- (b)
Rs. 1600

- (c)
Rs. 2600

- (d)
None of these

Answer: Option C

**Explanation** :

We know, Profit ∝ Investment × Time

Ratio of profit for Ankush and Vishal = 3000 × 7 : 5000 × 12 months = 7 : 20

Hence, share of Ankush = 7/27 × 5400 = 1400.

Share of Vishal = 5400 – 1400 = 4000.

Hence, the difference = 4000 – 1400 = 2600.

Hence, option (c).

Workspace:

**CRE 4 - Partnership | Arithmetic - Ratio, Proportion & Variation**

Three partners shared the profit in a business in the ratio 5 : 8 : 7. They had partnered for 14 months, 7 months and 8 months respectively. What was the ratio of their investments?

- (a)
5 : 8 : 7

- (b)
38 : 21 : 28

- (c)
20 : 64 : 49

- (d)
None of these

Answer: Option C

**Explanation** :

Let their investments be Rs. x for 14 months, Rs. y for 7 months and Rs. z for 8 months respectively.

We know, Profit ∝ Investment × Time

Hence, ratio of their profit, 5 : 8 : 7 = 14x : 7y : 8z.

Now, 14x/7y = 5/8 ⇒ y = 16/5 x

And, 14x/8z = 5/7 ⇒ z = 49/20 x

∴ x ∶ y ∶ z = x ∶ 16/5 x ∶ 49/20 x = 20 ∶ 64 ∶ 49

Alternately,

We know, ratio of their profit, 5 : 8 : 7 = 14x : 7y : 8z.

⇒ x : y : z = $\frac{5}{14}:\frac{8}{7}:\frac{7}{8}$= $\frac{56\times 5}{14}:\frac{56\times 8}{7}:\frac{56\times 7}{8}$ = 20 : 64 : 49

Hence, option (c).

Workspace:

**CRE 4 - Partnership | Arithmetic - Ratio, Proportion & Variation**

Ankush starts business with Rs. 10,500 and after 5 months, Vishal joins with Ankush as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B's contribution in the capital?

- (a)
Rs. 22,500

- (b)
Rs. 27,000

- (c)
Rs. 25,500

- (d)
Rs. 24,000

Answer: Option B

**Explanation** :

Let B's capital be Rs. x.

We know, Profit ∝ Investment × Time

Then, 2/3 = (10,500 × 12) / (x × 7)

⇒ x = $\frac{10,500\times 12\times 3}{7\times 2}$

⇒ x = 27,000.

Hence, option (b).

Workspace:

**CRE 4 - Partnership | Arithmetic - Ratio, Proportion & Variation**

A and B invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share is Rs. 1710, the total profit is:

- (a)
Rs. 2850

- (b)
Rs. 3000

- (c)
Rs. 3075

- (d)
Rs. 3152

Answer: Option B

**Explanation** :

Let the total profit be Rs. 100P.

After paying to charity, A's share = Rs. 95P × $\frac{3}{5}$ = Rs. 57P

Given, A's share is Rs. 57P = 1710

⇒ P = 1710/57 = 30

Total profit = 100 × 30 = 3000

Hence, option (b).

Workspace:

**CRE 4 - Partnership | Arithmetic - Ratio, Proportion & Variation**

A, B and C jointly engaged themselves in a business venture. It was agreed that A would invest Rs. 13,000 for 6 months, B, Rs. 16,800 for 5 months and C, Rs. 20,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 14,800. Calculate the share of B in the profit.

- (a)
Rs. 3800

- (b)
Rs. 5320

- (c)
Rs. 5600

- (d)
Rs. 5680

Answer: Option B

**Explanation** :

For managing, A received = 5% of Rs. 14,800 = Rs. 740.

Balance = Rs. (14,800 - 740) = Rs. 14,060.

Ratio of their investments = (13,000 × 6) : (16,800 × 5) : (20000 × 3) = 78000 : 84000 : 60000 = 13 : 14 : 10

∴ B's share = Rs. (14,060 × 14/37) = Rs. 5320.

Hence, option (b).

Workspace:

**CRE 4 - Partnership | Arithmetic - Ratio, Proportion & Variation**

A, B and C enter into a partnership in the ratio $\frac{7}{2}:\frac{4}{3}:\frac{6}{5}$. After 4 months, A increases his share 50%. If the total profit at the end of one year be Rs. 43,200, then B's share in the profit is:

- (a)
Rs. 4200

- (b)
Rs. 4800

- (c)
Rs. 7200

- (d)
Rs. 8000

Answer: Option D

**Explanation** :

Ratio of initial investments = $\frac{7}{2}:\frac{4}{3}:\frac{6}{5}$ = 105 : 40 : 36.

Let the initial investments be 105x, 40x and 36x.

∴ Ratio of profits of A : B : C = $(105x\times 4+\frac{150}{100}\times 105x\times 8)$ : $(40x\times 12)$ : $(36x\times 12)$ = 1680x : 480x : 432x = 35 : 10 : 9.

Hence, B's share = Rs. (43,200 × 10/54) = Rs. 8000.

Hence, option (d).

Workspace:

**CRE 4 - Partnership | Arithmetic - Ratio, Proportion & Variation**

A, B, C subscribe Rs. 1,00,000 for a business. A subscribes Rs. 8,000 more than B and B Rs. 10,000 more than C. Out of a total profit of Rs. 1,05,000, A receives:

- (a)
Rs. 25,200

- (b)
Rs. 35,700

- (c)
Rs. 40,800

- (d)
Rs. 44,100

Answer: Option D

**Explanation** :

Let C’s investment = x.

Then, B = x + 10,000 and A = x + 10,000 + 8,000 = x + 18,000.

So, x + x + 10,000 + x + 18,000 = 1,00,000

∴ 3x = 72,000

∴ x = 24,000

A : B : C = 42000 : 34000 : 24000 = 21 : 17 : 12.

∴ A's share = Rs.(1,05,000 × 21/50) = Rs. 44,100.

Hence, option (d).

Workspace:

**CRE 4 - Partnership | Arithmetic - Ratio, Proportion & Variation**

Ankush and Vishal entered into partnership with capitals in the ratio 4 : 5. After 3 months, Ankush withdrew 1/4th of his capital and Vishal withdrew 1/5th of his capital. The gain at the end of 10 months was Rs. 1520. Ankush's share in this profit is:

- (a)
Rs. 760

- (b)
Rs. 720

- (c)
Rs. 660

- (d)
Rs. 860

Answer: Option C

**Explanation** :

Let initial investment of Ankush = 4x and that of Vishal = 3x.

Ratio of profits of Ankush and Vishal = $[4x\times 3+(4x-\frac{1}{4}\times 4x)\times 7]$ : $[5x\times 3+(5x-\frac{1}{5}\times 5x)\times 7]$

= (12x + 21x) : (15x + 28x) = 33x : 43x = 33 : 43.

Ankush's share = Rs. (1520 × 33/76) = Rs. 660.

Hence, option (c).

Workspace:

**CRE 4 - Partnership | Arithmetic - Ratio, Proportion & Variation**

Ankush and Vishal started a partnership business investing some amount in the ratio of 3 : 5. Dinesh joined them after nine months with an amount equal to twice that of Vishal. In what proportion should the profit at the end of one year be distributed among Ankush, Vishal and Dinesh?

- (a)
3 : 5 : 2

- (b)
3 : 5 : 5

- (c)
6 : 10 : 5

- (d)
Data Inadequate

Answer: Option C

**Explanation** :

Let the initial investments of A and B be 3x and 5x.

A : B : C = (3x × 12) : (5x × 12) : (10x × 3) = 36 : 60 : 30 = 6 : 10 : 5.

Hence, option (c).

Workspace:

**CRE 4 - Partnership | Arithmetic - Ratio, Proportion & Variation**

Ankush, Vishal, Dinesh rent a pasture. Ankush puts 10 cows for 7 months, Vishal puts 12 cows for 5 months and Dinesh puts 15 cows for 3 months for grazing. If the rent of the pasture is Rs. 1050, how much must Dinesh pay as his share of rent?

- (a)
Rs. 270

- (b)
Rs. 300

- (c)
Rs. 330

- (d)
Rs. 360

Answer: Option A

**Explanation** :

A : B : D = (10 × 7) : (12 × 5) : (15 × 3) = 70 : 60 : 45 = 14 : 12 : 9.

∴ D's rent = Rs. (1050 × 9/35) = Rs. 270.

Hence, option (a).

Workspace:

**CRE 4 - Partnership | Arithmetic - Ratio, Proportion & Variation**

Ankush and Vishal started a business in partnership investing Rs. 40,000 and Rs. 30,000 respectively. After six months, Dinesh joined them with Rs. 40,000. What will be Vishal's share in total profit of Rs. 50,000 earned at the end of 2 years from the starting of the business?

- (a)
Rs. 18,000

- (b)
Rs. 19,000

- (c)
Rs. 20,000

- (d)
Rs. 15,000

Answer: Option D

**Explanation** :

A : B : D = (40,000 × 24) : (30,000 × 24) : (40,000 × 18) = 4 : 3 : 3.

∴ B's share = Rs. (50,000 × 3/10) = Rs. 15,000.

Hence, option (d).

Workspace:

**CRE 4 - Partnership | Arithmetic - Ratio, Proportion & Variation**

A began business with Rs. 1,250 and is joined afterwards by B with Rs. 3,750. When did B join if the profits at the end of the year are divided equally.

- (a)
After 6 months

- (b)
After 8 months

- (c)
After 4 months

- (d)
After 7 months

Answer: Option B

**Explanation** :

Let B joined for x months.

∴ P_{A }: P_{B }= I_{A }× T_{A} ∶ I_{B }× T_{B}

⇒ 1/1 = (1250 × 12)/(3750 × x)

⇒ x = 4

Hence, he joined after 12 - 4 = 8 months.

Hence, option (b).

Workspace:

**CRE 4 - Partnership | Arithmetic - Ratio, Proportion & Variation**

Nirmal and Kapil starting a business investing Rs. 9,000 and Rs. 12,000 respectively. After 6 months, Kapil withdrew half of his investment. If after a year, the total profit was Rs. 4,600 what was Kapil’s share in it?

- (a)
Rs. 2000

- (b)
Rs. 2600

- (c)
Rs. 1900

- (d)
Rs. 2300

Answer: Option D

**Explanation** :

Nirmal’s investment for 12 months = 9,000

Kapil average investment for 12 months = (12000 × 6 + 6000 × 6)/12 = 9,000

∴ Ratio of their profit = Ratio of their investment

⇒ Profit of Nirmal : Profit of Kapil = 9000 : 9000 = 1 : 1

Hence, Kapil’s profit = 1/2 × 4600 = 2300.

Hence, option (d).

Workspace:

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