P and Q enter into a partnership with investments of Rs.1400 and Rs.1800 respectively. They share half of the profit equally for running the business and the remaining profit in the ratio of their investments. If the difference in their shares of profits is Rs.47, what is the total profit?

Correct option is D

Let's assume the total profit is x Rs. Half of the profit is shared equally, so each gets x/2 × 1/2 = x/4 Rs. The remaining profit x/2 Rs is shared in the ratio of their investments, which is 1400:1800 or 7:9. Let P's share from the remaining profit be (7/16) × (x/2) and Q's share be (9/16) × (x/2). Now, we know the difference in their total shares is Rs.47: (x/4 + (7/16) ×(x/2)) - (x/4 + (9/16) ×(x/2)) = 47 Simplifying the equation: x/4 + 7x/32 - (x/4 + 9x/32) = 47 7x/32 - 9x/32 = 47 -2x/32 = 47 -x/16 = 47 x = 47 × -16 x = 752 So, the total profit is Rs. 752.