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CAT 2018 Slot 2 — QA Question 5

Simple and Compound InterestEasy

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 & solution

Answer: 4000

Solution

Easy

Compare the two lending scenarios. The only change in the second is an extra Rs. Y\text{Rs.}\,Y lent to Ishan at 10%10\%, so that extra retained interest is 0.1Y0.1Y — this gives YY at once. Then equate Gopal's net interest to Ankit's interest to get XX.

1

Find YY from the increase. Lending Rs. Y\text{Rs.}\,Y more at 10%10\% adds exactly 0.1Y0.1Y to Gopal's retained interest, and this increase is Rs. 150\text{Rs.}\,150.

0.1 Y=150⇒ Y=1500\begin{aligned} &0.1\,Y = 150\\ &\Rightarrow\ Y = 1500 \end{aligned}
2

Set up the equal-interest condition. Ankit earns 0.08X0.08X on the loan to Gopal. Gopal earns 0.10(X+Y)0.10(X+Y) from Ishan and pays Ankit 0.08X0.08X, so his net interest is 0.10(X+Y)−0.08X0.10(X+Y)-0.08X. These are equal:

0.10(X+Y)−0.08X=0.08X⇒ 0.10X+0.10(1500)−0.08X=0.08X(sub Y=1500)⇒ 0.02X+150=0.08X\begin{aligned} &0.10(X+Y)-0.08X = 0.08X\\ &\Rightarrow\ 0.10X + 0.10(1500) - 0.08X = 0.08X \quad\text{(sub }Y=1500)\\ &\Rightarrow\ 0.02X + 150 = 0.08X \end{aligned}
3

Solve for XX, then add.

0.06X=150⇒ X=2500⇒ X+Y=2500+1500=4000\begin{aligned} &0.06X = 150\\ &\Rightarrow\ X = 2500\\ &\Rightarrow\ X+Y = 2500+1500 = 4000 \end{aligned}
X+Y=4000X+Y = 4000
CAT 2018 Slot 2 QA Q5: 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 — Solution | TheCATExam