Two partner’s P and Q started a business by investing Rs. 15000 and Rs. 20000 respectively. After 6 months, Q withdrew some amount of his investment. At the same time, a third friend R joined the business by investing the same amount which Q has withdrawn. At the end of the year, Q and R distributed their profits in the ratio 5 ∶ 3. If the total profit for the year was Rs. 15400, find the amount withdrawn?

Option 1 : Rs. 15000

Let the amount withdrawn = Rs. X

P invested his entire amount Rs. 15000 for the whole 12 months period

Q invested Rs. 20000 for 6 months and (20000 - X) for 6 months

R invested Rs. X for 6 months (As investment by R is similar to the amount withdrawn by Q)

Given that the ratio of the profits of Q and R is 5 ∶ 3

We know that the ratio of the profit of Q and R will be equal to the ratio of product of their investments and Time period

/6X = 5/3

⇒ (240000 - 6X)/6X = 5/3

⇒ (720000 - 18X) = 30X

⇒ 48X = 720000

⇒ X = 720000/48

⇒ X = 15000