 # Ratio & Proportion (10)

1. A and B entered into partnership with capitals in the ratio 4 : 5. After 3 months, A withdrew ¼ of his capital and B withdrew 1/5 of his capital. At the end of 10 months, the gain was Rs. 760. What is A’s share in the profit?
1. 310
2. 330
3. 370
4. 350

Explanation :-

Let the initial capital of A= 4x  &  B = 5x
A’s Share in profit : B’s Share in profit = (4x*3) + (3/4)*(4x)*7 : (5x*3)+ (4/5)*(5x)*7
A’s Share in profit : B’s Share in profit  = (12 + 21) : (15 + 28) = 33 : 43
A’s share = 760 * 33/76 = 330

2. A starts a business with Rs. 3500. After 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. B’s contribution in the capital is
1. 7000
2. 8000
3. 9000
4. 10000

Explanation :-

Let B’s Investment = Rs. x
(3500 * 12) / 7x = 2/3
14126000
Rs. 9000

3. A, B and C shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?
1. 10:12:14
2. 12:24:28
3. 20:22:12
4. 20:49:64

Explanation :-

Let A’s Investment = Rs. x for 14 months,
B’s Investment = Rs. y for 8 months,
C’s Investment = Rs. z for 7 months,
Therefore , 14x : 8y : 7z = 5 : 7 : 8.
14x / 8y = 5 / 7 => 98x = 40y  => y = (49 / 20)x
&
14x / 7z = 5/8   => 112x = 35z    => z =  (16 / 5)x .
Therefore  x : y : z = x : 49/20 x : 16/5 x = 20 : 49 : 64.

4. A and B started a partnership business investing capital in the ratio of 3 : 5. C joined in the partnership after six months with an amount equal to that of B. At the end of one year, the profit should be distributed among A, B and C in — proportion.
1. 10 : 5 : 4
2. 5 : 3 : 4
3. 3 : 4: 5
4. 6 : 10 : 5

Explanation :-

Let the initial capital of A = 3x   &   Let the initial capital of B = 5x
Therefore , C’s Investment = 5x ( for 6 months)
Ratio of their Profits = A : B : C
A : B : C = (3x * 12) : (5x * 12) : (5x * 6) = 36 : 60 : 30 = 6 : 10 : 5

5. A & B partner in a business , A contribute 1/4 of the capital for 15 months & B received 2/3 of the profit . For how long B’s money was used
1. 12 months
2. 10 months
3. 14 months
4. 16 months

Explanation :-

B’s Share in Profit =  2/3 , Therefore,  A’s Share in Profit = 1/3
A’s Share in Profit : B’s Share in Profit  = 1/3 : 2/3 = 1: 2
Let the total capital = x , Therefore  A’s capital = x/4   &   B’s capital = x – x/4 = 3x/4
Let B invested for y months
Then A’s investment : B’s investment = (x / 4) * 15 : (3x / 4) * b = 1 : 2
=> 15/4 : 3b/4 = 1 : 2
=> 15 : 3b = 1 : 2
=> 5 : b = 1 : 2
=> 5/b = 1/ 2
=> b = 5*2 = 10