X, Y and Z start a partnership firm with capital investment in the ratio 1/2 : 1/3 : 1/4. After two months, X withdraws half of his capital and after 10 months, a profit of Rs. 10,500 is divided among them. What is Y's share?

Convert the given capital ratio of 1/2 to 1/3 to 1/4 into whole numbers by finding the common denominator, which yields a ratio of 6 to 4 to 3. Since X withdraws half of his capital after two months, X's capital is 6 units for 2 months and 3 units for 10 months, while Y and Z keep their full capital for the entire 12 months. The effective capital ratio is (6 x 2 + 3 x 10) to (4 x 12) to (3 x 12), which equals 42 to 48 to 36, simplifying to 7 to 8 to 6. The total parts equal 21, so Y's share of the Rs. 10500 profit is (8 divided by 21) x 10500, which is Rs. 4000.

• Thanks
• Wrong explanation