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Question 28 : 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. [TITA]

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Let us draw a flow diagram to understand the transaction

Gopal receives 10% of X + Y from Ishan as interest, from which he pays the interest of 8% of X to Ankit

So, Gopal would gain 2% of X + 10% of Y as interest and Ankit would gain 8% Interest

Its given that both the interest values are same, so 2% X + 10% Y = 8% X

3% X = 5% Y --- (1)

Its also given that, if Gopal lend Rs. X + 2Y to Ishan at 10% interest, the net interest retained would increase by Rs. 150

So, the increase in 10% Y accounts for Rs. 150

10% Y = 150 => Y = Rs. 1500

Substituting the value in (1), we get 5 × 1500 = 3 × X => X = 2500

So, X + Y = 2500 + 1500 = Rs 4000

The question is **"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. [TITA]"**

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