A started a business with Rs.26000. After 3 months B joined him with Rs.16000. After some more time C joined them with Rs.25000. At the end of the year, out of a total profit of Rs.15453, C gets Rs.3825 as his share. How many months after B joined the business did C join?

A invests Rs.26000 for 12 months, B invests Rs.16000 for (12-3)=9 months. Let C invest Rs.25000 for t months. Profit sharing ratio = A : B : C = 26000×12 : 16000×9 : 25000×t = 312000 : 144000 : 25000t = 312 : 144 : 25t. Total profit = 15453, C's share = 3825. So (25t)/(312+144+25t) × 15453 = 3825. 25t/(456+25t) × 15453 = 3825. 25t/(456+25t) = 3825/15453 = 5/20.21? Actually 15453/3825 = 4.04. Let's solve: 3825×(456+25t) = 15453×25t. 1744500 + 95625t = 386325t. 1744500 = 290700t. t = 1744500/290700 = 6. So C invested for 6 months. B joined after 3 months, so B joined at month 3. If C invested for 6 months and started at the end, C joined at month 12-6 = 6. Time after B joined = 6 - 3 = 3 months. The claimed answer D is correct.