Ratio & Proportion (8)

1. Suresh started a business with Rs.20,000. Kiran joined him after 4 months with Rs.30,000. After 2 months, Suresh withdrew Rs.5,000 of his capital and 2 more months later, Kiran brought in Rs.20,000 more. What should be the ratio in which they should share their profits at the end of the year?
1. 21:32
2. 32:21
3. 12:17
4. 17:12

Explanation :-

Suresh’s Total investement = 20000 for initial 6 months and 15000 for the next 6 months. = ( 20000*6 + 15000*6)
Kiran’s Total investement = 30000 for 4 months and Rs.50000 for next 4 months = (30000*4 + 50000*4)
Suresh : Kiran = ( 20000*6 + 15000*6) : (30000*4 + 50000*4) = (20*6 + 15*6) : (30*4 + 50*4)
= (20*3 + 15*3)  : (30*2 : 50*2)
= 105 : 160
= 21 : 32

2. Kamal started a business with Rs.25000 and after 4 months, Kiran joined him with Rs.60000. Kamal received Rs.58000 including 10% of profit as commission for managing the business. What amount did Kiran receive?
1. 75000
2. 70000
3. 72000
4. 78000

Explanation :-

Ratio of the profits = 25000*12 : 60000*8 = 5 : 8
Let the total profit = x.
Then Kamal received=  10x/100 = x/10 as commission for managing the business
Remaining profit = x – (x/10) = 9x/10 which is shared in the ration 5:8
Kamal’s share = x/10 + (9x/10) * (5/13) = 58000
x + 9x(5 / 13) = 580000
x(1 + 45/13) = 580000
x ( 58/13) = 580000
x ( 1/13) = 10000
x = 130000
Kiran’s share = 130000 – 58000 = 72000

3. A and B started a partnership business investing Rs. 20,000 and Rs. 15,000 respectively. C joined them with Rs. 20,000 After six months. Calculate B’s share in total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
1. 7500
2. 8500
3. 9000
4. 8000

Explanation :-

A : B : C = (20,000 x 24) : (15,000 x 24) : (20,000 x 18) = 4 : 3 : 3
B’s Share = 25000 * (3/10) = Rs. 7500

4. A starts a business with a capital of Rs. 85,000. B joins in the business with Rs.42500 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?
1. 5 months
2. 6 months
3. 7 months
4. 8 months

Explanation :-

lets assume B joined for x months .
Therefore,
( 85000 * 12 ) / (42500 * x) = 3.
x = (85000 * 12) / (42500 * 3)
x = 8.
Therefore,  B joins for 8 months.

5. A starts a business with Rs.40,000. After 2 months, B joined him with Rs.60,000. C joined them after some more time with Rs.1,20,000. At the end of the year, out of a total profit of Rs.3,75,000, C gets Rs.1,50,000 as his share. How many months after B joined the business, did C join?
1. 4 months
2. 5 months
3. 6 months
4. 7 months

Explanation :-

Let’s assume C joins for x months .
A : B : C = (40000*12) : (60000 * 10) : (120000*x)
=> (40*12) : (60*10) : (120x)
=> 40 : 5*10 : 10x => 4 : 5 : x
C’s share = (375000 * x) / (9 + x) = 150000
=> (375x) / (9 + x) = 150
=> 15x = 6(9 + x)
=> 5x = 18 + 2x
=> 3x = 18
=> x = 6
B joins for 10 month  & C joins for 6 months
Therefore , C joined after 4 months when B joined