Bunty invested 3 different amounts Rs. x, y and z at rate of 25%, 10% and 15% respectively for 2 years compounded annually. Compound interest at Rs. x is 465 more than than 50% of the compound interest at Rs. z, whereas the compound interest at Rs. y is 960 less than the 50% of the compound interest at Rs. z. If y – x = Rs. 10,000, then which of the following option's value is less than the total amount invested? (Total amount invested = (x + y + z) (i) 56,525 (ii) 60.658 (iii) 61,620 (iv) 62,650 (v) 65,600

Using the compound interest formula A = P(1 + R/100)^T, the multipliers for x, y, and z are (1.25)^2 = 1.5625, (1.1)^2 = 1.21, and (1.15)^2 = 1.3225, respectively; this means the interests are 0.5625x, 0.21y, and 0.3225z. Solving the system of equations 0.5625x - 0.16125z = 465, 0.21y - 0.16125z = -960, and y - x = 10000 gives x = 10000, y = 20000, and z = 30000. The total amount invested is x + y + z = 60000, meaning the values 56525, 60658, and 61620 are all less than this total.

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