A sum of ₹22,100 was divided between Timir and Monali in such a way that if both invested their shares at 10% compound interest per annum, the amount payable on maturity to Monali after 18 years would be the same as the amount payable on maturity to Timir after 20 years. What was the share of Monali in the initial sum?

Solution

Let the share of Monali and Timir be x and (22100 - x) respectively. Amount payable in the case of Monali. = x (1 + 10/100)¹⁸ Amount payable in case of Timir. (22100-x) (1 + 10/100)²⁰ According to the question, (22100 - x) (1 +10/100)²⁰= x (1 + 10/100)¹⁸ (22100-x) (1 + 10 /100) ^20-18 = x (22100-x) (1 + 10/100)² = x (22100-x) x 1.21 = x 26741-1.21x = x 2.21x=26741 x=26741/2.21 x = 12100 The initial share of Monali was Rs. 12,100.