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A started business with Rs. 4,500 and B joined afterward with Rs. 3,000. If the profits at the end of one year were divided in the ratio 2 : 1, respectively, then B would have joined A for business after

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1 month

2 months

3 months

4 months

answer is C.

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Detailed Solution

Given that A started business with Rs. 4,500 and B joined afterward with Rs. 3,000 and the profits at the end of one year were divided in the ratio 2 : 1.
Then,
A's 1 month's investment

= Rs . (4500 \times 12)

\Rightarrow

A's 1 month's investment

= Rs . 54, 000

Let B join after

x

months.

∴

B's 1 month's investment

= Rs . 3, 000 (12 - x)

By the given condition,

54, 000 : 3, 000 (12 - x) = 2 : 1

\Rightarrow \frac{18}{12 - x} = 2

\Rightarrow 18 = 24 - 2 x

\Rightarrow 2 x = 6

\Rightarrow x = 3

months
Thus, B joined after 3 months.
Therefore, the correct option is 3.

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