Question : A invests Rs. 64,000 in a business. After a few months, B joined him with Rs. 48,000. At the end of the year, the total profit was divided between them in the ratio 2 : 1. After how many months did B join?
Option 1: 8
Option 2: 4
Option 3: 6
Option 4: 7
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Correct Answer: 4
Solution : Let the number of months after which B joined as $x$ months. Therefore, A's investment was for 12 months and B's investment was for $(12 - x)$ months. The ratio of A's investment to B's investment is equal to the ratio of their profits. $⇒\frac{(64000 \times 12)}{(48000 \times (12 - x)) }= \frac{2}{1}$ $⇒\frac{(4 \times 12)}{(3 \times (12 - x)) }= \frac{2}{1}$ $⇒\frac{8}{(12 - x)}= 1$ $⇒x= 12 - 8 = 4$ months Hence, the correct answer is 4.
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