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A started a business with ₹63,000 and is joined afterwards by B with ₹1,08,000. After how many months did B join if the profits at the end of the year
Question

A started a business with ₹63,000 and is joined afterwards by B with ₹1,08,000. After how many months did B join if the profits at the end of the year are divided equally ?

A.

3

B.

4

C.

5

D.

6

Correct option is C

Given:
A's investment = ₹ 63,000
B's investment = ₹ 1,08,000
Profits are divided equally at the end of the year.
Formula Used:
Ratio of Profits = Ratio of (Investment × Time)
Solution:
Let B's investment period be x months.
A invested his money for the full year, which is 12 months.
The ratio of their profit shares is:
​A′s ProfitB′s Profit=63000×12108000×x\frac{A's\ Profit}{B's\ Profit} = \frac{63000 × 12}{108000 × x}​​
Since profits are equal, the ratio is 1:1.
​1=63000×12108000×x1 = \frac{63000 × 12}{108000 × x}​​

​1=63×12108×x1 = \frac{63 × 12}{108 × x}​​

​1=756108x1 = \frac{756}{108x}​​
108x = 756
​x=756108x = \frac{756}{108}​​
x = 7
This means B invested for 7 months.
Therefore, B joined after: 12 - 7 = 5 months.
Final Answer
So the correct answer is (c)

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