**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.

**Show Answer**

Correct Answer: 4000

Interest to be repaid to Ankit at the end of the year = 0.08X

Interest that Gopal would receive from Ishan in two cases are as given.

Case I: if he lends X + Y

Interest received = (X + Y) × 0.1 = 0.1X + 0.1Y

Interest retained by Gopal after paying to Ankit

= (0.1X + 0.1Y) – (0.08X) = 0.02X + 0.1Y

Given that Interest retained by Gopal is same as that accrued by Ankit

=> (0.02X + 0.1Y) = 0.08X

=> Y = 0.6X

Case II: if he lends X + 2Y

Interest received = (X + 2Y) × 0.1 = 0.1X + 0.2Y

Interest retained by Gopal after paying to Ankit

= (0.1X + 0.2Y) – (0.08X) = 0.02X + 0.2Y

Given that interest retained by Gopal would increase by 150

=> (0.02X + 0.2Y) – (0.02X + 0.1Y) = 150

0.1Y = 150

=> Y = 1500 and X = 1500×0.6= 2500

Hence X + Y = 2500 + 1500 = 4000

Interest to be repaid to Ankit at the end of the year = 0.08X

Interest that Gopal would receive from Ishan in two cases are as given.

Case I: if he lends X + Y

Interest received = (X + Y) × 0.1 = 0.1X + 0.1Y

Interest retained by Gopal after paying to Ankit

= (0.1X + 0.1Y) – (0.08X) = 0.02X + 0.1Y

Given that Interest retained by Gopal is same as that accrued by Ankit

=> (0.02X + 0.1Y) = 0.08X

=> Y = 0.6X

Case II: if he lends X + 2Y

Interest received = (X + 2Y) × 0.1 = 0.1X + 0.2Y

Interest retained by Gopal after paying to Ankit

= (0.1X + 0.2Y) – (0.08X) = 0.02X + 0.2Y

Given that interest retained by Gopal would increase by 150

=> (0.02X + 0.2Y) – (0.02X + 0.1Y) = 150

0.1Y = 150

=> Y = 1500 and X = 1500×0.6= 2500

Hence X + Y = 2500 + 1500 = 4000

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