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A started a business investing Rs. 3000. After 3 months, B joined the business investing Rs. 2000. After some more time, C joined the business investing Rs. 1500. At the end of the year, profit from the business was Rs. 16000 and share of C was Rs.1600 out of the profit. For how many months C invested in the business?

A started a business investing Rs. 3000. After 3 months, B joined the business investing Rs. 2000. After some more time, C joined the business investing Rs. 1500. At the end of the year, profit from the business was Rs. 16000 and share of C was Rs.1600 out of the profit. For how many months C invested in the business? Correct Answer 4

GIVEN:

A started a business investing Rs. 3000. After 3 months, B joined the business investing Rs. 2000. After some more time, C joined the business investing Rs. 1500. At the end of the year, profit from the business was Rs. 1600 and share of C was Rs. 16000 out of the profit.

CONCEPT:

Profit will be shared according to the Investment and the time for which the investment is done.

CALCULATION:

Suppose C invested in the business for ‘x’ months.

So,

Ratio in which the profit will be shared among A, B and C

= (3000 × 12) : (2000 × 9) : (1500 × x)

= 360 : 180 : 15x

= 24 : 12 : x

Now,

Share of C is given to be Rs. 1600 out of Rs. 16000.

Hence,

x/(24 + 12 + x) = 1600/16000

⇒ x/(36 + x) = 1/10

⇒ 10x = 36 + x

⇒ x = 4

∴ C invested amount for 4 months.

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