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.

Answer 1

Correct Answer: 4000

Let Gopal borrow Rs. \( X \) at an 8% annual interest rate. He then lends Rs. \( (X + Y) \) at a 10% annual interest rate.

Interest Gopal pays Ankit: \( 0.08X \) 
Interest Gopal earns from Ishan: \( 0.10(X + Y) \)

Since the net interest retained by Gopal is the same as that paid to Ankit:

\[ 0.10(X + Y) - 0.08X = 0.08X \] \[ 0.10X + 0.10Y - 0.08X = 0.08X \] \[ 0.02X + 0.10Y = 0.08X \Rightarrow 0.10Y = 0.06X \Rightarrow Y = 0.60X \]

Case 2: Gopal lends Rs. \( X + 2Y \) to Ishan

Interest earned: \( 0.10(X + 2Y) \) 
Interest paid: \( 0.08X \) 
Net interest: \( 0.10(X + 2Y) - 0.08X \)

Increase in net interest = Rs. 150, so:

\[ \left[ 0.10(X + 2Y) - 0.08X \right] - \left[ 0.10(X + Y) - 0.08X \right] = 150 \] \[ 0.10X + 0.20Y - 0.08X - (0.10X + 0.10Y - 0.08X) = 150 \] \[ 0.20Y - 0.10Y = 150 \Rightarrow 0.10Y = 150 \Rightarrow Y = 1500 \]

Since \( Y = 0.60X \Rightarrow 0.60X = 1500 \Rightarrow X = 2500 \)

Therefore, \( X + Y = 2500 + 1500 = \boxed{4000} \)