A starts a business with a capital of Rs. 85,000. B joins in the business with Rs.42500 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?Options5786

Let's solve the problem step by step:

1. We know that A starts the business with a capital of Rs. 85,000.
2. B joins the business after some time with a capital of Rs. 42,500.
3. The profits at the end of the year are divided in the ratio of 3:1 between A and B.
4. To find out for how much period B joins the business, we need to calculate the ratio of their capitals.
   • The ratio of A's capital to B's capital is 85,000 : 42,500, which simplifies to 2:1.
   • Since the profit ratio is 3:1, we can conclude that B joined the business for 1/3 of the year.
5. To calculate the period for which B joined, we need to multiply the total time period by the fraction representing B's share of the profit ratio.
   • Let's assume the total time period is T.
   • B's share of the profit ratio is 1/4 (1 out of 4 parts).
   • So, B joined the business for (1/4) * T.
6. We need to find the value of T.
   • Since B joined the business for 1/3 of the year, we can set up the equation: (1/4) * T = (1/3) * T.
   • Solving this equation, we find that T = 12.
7. Therefore, B joined the business for (1/4) * 12 = 3 months.

So, B joined the business for 3 months.