P invested Rs. 7,000 at a simple interest rate of 22% per annum, while Q invested an unknown sum at a compound interest rate of 20% per annum (compounded annually). If the interest earned by P after 2 years was twice the interest earned by Q, find the amount invested by Q.

ATQ, Simple interest = (Sum × rate of interest × time period) ÷ 100 Interest earned by P = (7000 × 22 × 2) ÷ 100 = Rs. 3,080 So, interest earned by Q = 3080 ÷ 2 = Rs. 1,540 Let the sum invested by P be Rs. 'p'. Amount at the end of two years in case of compound interest = Sum × {1 + (rate/100) }time period ATQ; 1540 + p = p × {1 + (20/100) }2 Or, 1540 + p = p × (1.2)2 Or, 1540 + p = 1.44p Or, 1540 = 0.44p So, p = (1540/0.44) = 3500 So, sum invested by Q = Rs. 3,500