A began a business with ₹ 2250 and was joined afterwards

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A began a business with ₹ 2250 and was joined afterwards by B with ₹ 2700. If the profits at the end of the year were divided in the ratio of 2 : 1, after how much time B joined the business ?

1. 5 months
2. 6 months
3. 3 months
4. 7 months
5. None of the above

Correct Option: D

Let B remained in the business for N months. Then,
A : B = (2250 x 12) : (2700 x N)
⇒ 2 : 1 = (27000 : 2700N) = (10 : N)
∴ 10/N = 2/1 [ ∵ Ratio of profit is 2 : 1]
⇒ 2N = 10
∴ N = 10/2 = 5
Clearly, B joined after (12 - 5) = 7 months.