Amit and Vikas are partners in a business. They invest in the ratio 4:7, at the end of 6 months Vikas withdraws. If they receive profits at the end of year in the ratio of 2:3, find how long Amit’s investment was used?

In partnership problems, profit is distributed in proportion to investment × time. Amit invests 4x for 12 months = 48x months. Vikas invests 7x for 6 months = 42x months. Profit ratio 2:3 means Amit gets 2 parts, Vikas gets 3 parts. Setting up: 48x/42x = 2/3 gives 48/42 = 8/7. Solving gives Amit's time = 7 months. Option D is correct.