## Examples

Question – Raj invested Rs 76000 in a business. After few months Monty joined him and invests Rs 57000. At the end of year both of them share the profits at the ratio of 2:1. After how many months Monty joined Raj ?

### Solution –

We can simply compute per month investment of both partnership

Raj invested Rs 76,000 for 12 months and Monty invested Rs 57,000 for x months.

Now 76000 × 12 / 57000 × x = 2 :1

⇒ 76 × 12 / 2 = 57x

⇒ x = 8

So Monty invested his money for 8 months and he joined after 4 months.

Question – A and B started a business by investing money in ratio of 5:6. C joined them after few months by sharing an amount equal to B’s share. At the end of year 20% profit was earned which was equal equal to Rs 98,000. How much money was invested by C ?

### Solution –

= First of all we will calculate the weighted ratios

⇒ A = 5 × 12 = 60

⇒ B = 6 × 12 = 72
⇒ C = 6 × 6 = 36
Total investment at the end of year = 98000 × 100/20 = Rs 4,90,000
⇒ Investment by C = 490000 × 36 / 168 × 2 = Rs 210000

Question –A, B and C shared profits in ratio of 5:7:8. They partnered for 14 months, 8 months and 7 months respectively. What was he ratio of their investments ?

### Solution –

Simply multiply profit sharing ratio with investment ratio to get investment amount ratio.

Let X is the total investment

⇒14 x = 5
⇒ 8 x = 7
⇒ 7x = 8

⇒ Final investment ratio = 20 : 49 : 64

Question – Sita and Geeta started a business by investing Rs. 120000 and Rs.135000 respectively. Find the share of each out of an annual profit of Rs. 35700.

### Solution :-

When investors are there for the different duration of time in the business , then the investments are calculated for a unit of time by having ( investment x number of units of time) . Now gain or loss is divided in the ratio of these investments.

Question – Ravi started a business by investing Rs.36000. After 3 months Shayam joined him by investing Rs.36000. Find the share of each in the annual profit of Rs. 37100.

### Solution –

Now let us do some questions:

Question – Sony , Mony and Tony start a business each investing Rs.20000. After 5 months Sony withdrew Rs.5000, Mony withdrew Rs.4000 and Tony added Rs.6000 more. At the end of the year, a total profit Of Rs. 69900 was recorded. Find the share of each?

### Solution –

Question – Sheela started a business with Rs. 21000 and is joined afterwords by Reema with Rs 36000. After how many months did Reema join if the profits at the end of the year are divided equally?

### Solution –

Question – X and Y invested in a business. They earned some profit which they divided in the ratio of 2:3. If X invested Rs. 40000. Find the amount invested by Y?

### Solution –

Question – A , B , C contract a work for Rs .1100.A and B together are to do 7/11 of the work . What is C’s share ?

### Solution –

Question – Mohinder and Surinder entered into a partnership investing Rs. 12000 and Rs. 9000 respectively . After 3 months , Sudhir joined them with an investment of Rs.15000. What is the share of Sudhir in a half yearly profit of Rs. 9500?

### Solution –

Question – In a partnership , A invests 1/6 of the capital for 1/6 of the time , B invests 1/3 of the capital for 1/3 of the time and C , the rest of the capital for the whole time. What is the share of B in the profit f Rs. 4600.

### Solution –

Question – Three partners 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?

### Solution –

Let the first partner invests Rs x for 14 months, second partner invests Rs.y for 8 months, Rs z for 7 months.