Sum of principal amounts

Question

Gopal borrows Rs. X from Ankit at 8% annual interest. He then adds Rs. Y of his own money and lends Rs. X+Y to Ishan at 10% annual interest. At the end of the year, after returning Ankit’s dues, the net interest retained by Gopal is the same as that accrued to Ankit. On the other hand, had Gopal lent Rs. X+2Y to Ishan at 10%, then the net interest retained by him would have increased by Rs. 150. If all interests are compounded annually, then find the value of X + Y.

Accepted Answer

4000. Interest paid to Ankit $= 0.08X$. Interest received from Ishan $= 0.10(X + Y)$. Net interest retained by Gopal $= 0.10(X + Y) - 0.08X = 0.02X + 0.10Y$. Given that net interest retained by Gopal equals interest accrued to Ankit: $$0.02X + 0.10Y = 0.08X \implies 0.10Y = 0.06X \implies X = \frac{5}{3}Y$$ Second condition: If Gopal lends $X + 2Y$ at 10%, net interest increases by 150: Additional interest $= 0.10(Y) = 150 \implies Y = 1500$. Then $X = \frac{5}{3}(1500) = 2500$. Value of $X + Y = 2500 + 1500 = 4000$.

Answer

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Sum of principal amounts

Explanation

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