A began business with Rs. 4,500 and was joined afterward by B with Rs. 5,400. If the profit at the end of the year was divided in the ratio of 2:1, then the time of joining B was after:

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8 months

9 months

7 months

5 months

answer is B.

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Detailed Solution

Given,
Principal of A, (P)= Rs.4500
Time of A, (T)= 12 months (1 year =12 months)
Principal of B, (p)= Rs.5400
Ratio of the profit = 2: 1
Let B remained in the business for

x

months.
Then,

\frac{Profit earned by A}{Profit earned by B} = \frac{P \times T}{p \times t}

\Rightarrow \frac{Profit earned by A}{Profit earned by B} = \frac{4500 \times 12}{5400 \times x}

\Rightarrow \frac{Profit earned by A}{Profit earned by B} = \frac{54000}{5400 x}

\Rightarrow \frac{Profit earned by A}{Profit earned by B} = \frac{10}{x}

From the given,

\frac{10}{x} = \frac{2}{1}

\Rightarrow

2 x = 10

\Rightarrow

x = 5

Thus, B remained in the business for 5 months.
Then B joined the business after (12-5) = 7 months later.
Thus, B joined 7 months later.
Therefore, the correct option is 2.

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