 # Ratio & Proportion (9)

1. A and B invest in a business in the ratio 3: 2. Assume that 5% of the total profit goes to charity. If A’s share is Rs. 855, what is the total profit?
1. 1400
2. 1500
3. 1600
5. 1200

Explanation :-

Let  the total profit be Rs. x.
Charity = 5% of x
Profit divided between A & B = 95% of x
A’s profit = 855 , Therefore
(95x/100) * (3/5) = 855
95x/100 = 855*5/3
95x/100 = 1425
x = 1425 * 100/95 = 1500
Therefore , the total profit = Rs. 1500

2. A, B and C invest in a partnership in the ratio: 7/2, 4/3, 6/5. After 4 months, A increases his share 50%. If the total profit at the end of one year be Rs. 21,600, then what is B’s share in the profit?
1. Rs. 2000
2. Rs. 3000
3. Rs. 4000
4. Rs. 5000

Explanation :-

Ratio of the initial investment = 7/2 : 4/3 : 6/5 = 105 : 40 : 36
Therefore,
Let the initial investments of A = 105x, B = 40x  &  C = 36x
As ,  A increases his share by 50% after 4 months
New Ratio = (105x + 4) + (105× (150/100) ×8) : (40x × 12) : (36x × 12)
=> 35 : 10 : 9
B’s share = 21600 × (10/54) = Rs. 4000

3. A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 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. 7400. What is the share of B in the profit.
1. 2660
2. 1000
3. 2300
4. 4000

Explanation :-

As A will receive extra 5% of the total profit = 5% of 7400 = 5*7400/100 = 370
Remaining amount = 7400-370 = 7030
Ratio of their investments = 6500*6 : 8400*5 : 10000*3
=> 65*6 : 84*5 : 100*3 = 13 : 14 : 10
B’s Share in Profit = 7030 * (14/37) = 190*14 = 2660

4. A, B, C subscribe Rs. 50,000 for a business. If A subscribes Rs. 4000 more than B and B Rs. 5000 more than C, out of a total profit of Rs. 35,000, what will be the amount A receives?
1.. 14200
2. 14700
3. 14800
4. 14500

Explanation :-

Total amount invested = 50000
Let C’s investment = Rs. x.
Therefore B’s investment = 5000 + x ,
A’s investment = 4000 + 5000 + x = 9000 + x
According to Question
x + (5000 + x) + (9000 + x) = 50000
=> 3x + 14000 = 50000
=> 3x = 50000 – 14000 = 36000
=> x = 36000/3 = 12000
Therefore , C’s investment = x = 12000 ,
B’s investment= 5000 + x = 17000,
A’s investment = 9000+x = 21000
Ratio of the investment of A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12
A’s share = 35000 * 21/50 = 700*21 = 14700

5. A, B, C rent a pasture. If A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing and the rent of the pasture is Rs. 175, then how much amount should C pay as his share of rent?
1. 45
2. 35
3. 55
4. 60