Arithmetic

Simple & Compound Interest

Medium

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 $X+Y$ .

Entered answer:

✅ Correct Answer: 4000

Gopal is essentially acting as a "middleman" in this lending scenario:

He borrows Rs. X from Ankit at 8% annual interest

He lends Rs. (X + Y) to Ishan at 10% annual interest

His profit = Interest received from Ishan - Interest paid to Ankit

Since we're dealing with one year, compound interest = simple interest

Interest Gopal owes to Ankit:

Amount borrowed = Rs. X

Interest rate = 8% per annum

Interest owed = $0.08X$

Case I: When Gopal lends (X + Y) to Ishan

Amount lent = Rs. (X + Y)

Interest rate = 10% per annum

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

Net interest retained by Gopal:

Net Interest = Interest Received - Interest Paid

Net Interest = $(0.1X + 0.1Y) - 0.08X = 0.02X + 0.1Y$

The problem states: "The net interest retained by Gopal equals the interest accrued to Ankit"

This means:

$0.02X + 0.1Y = 0.08X$

$0.1Y = 0.08X - 0.02X$

$0.1Y = 0.06X$

$Y = 0.6X$

Key insight: Y is 60% of X

Case II: When Gopal lends (X + 2Y) to Ishan

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

Net interest = $(0.1X + 0.2Y) - 0.08X = 0.02X + 0.2Y$

The problem states: "Net interest would increase by Rs. 150"

This means:

$(0.02X + 0.2Y) - (0.02X + 0.1Y) = 150$

$0.1Y = 150$

$Y = 1500$

Since $Y = 0.6X$ and $Y = 1500$ :

$1500 = 0.6X$

$X = \dfrac{1500}{0.6} = 2500$

Therefore:

X = Rs. 2500

Y = Rs. 1500

X + Y = Rs. 4000

Answer: X + Y = Rs. 4000

CAT 2020 Slot 1

Veeru invested Rs 10000 at 5% simple annual interest, and exactly after two years, Joy invested Rs 8000 at 10% simple annual interest. How many years after Veeru's investment, will their balances, i.e., principal plus accumulated interest, be equal?

CAT 2021 Slot 1

Anil invests some money at a fixed rate of interest, compounded annually. If the interests accrued during the second and third year are $₹ 806.25$ and $₹ 866.72,$ respectively, the interest accrued, in INR, during the fourth year is nearest to

CAT 2020 Slot 3

A person invested a certain amount of money at $10\%$ annual interest, compounded half-yearly. After one and a half years, the interest and principal together became Rs $18522$ . The amount, in rupees, that the person had invested is

CAT 2019 Slot 1

Amala, Bina, and Gouri invest money in the ratio $3: 4: 5$ in fixed deposits having respective annual interest rates in the ratio $6: 5:4$ . What is their total interest income (in Rs) after a year, if Bina's interest income exceeds Amala's by Rs $250$ ?

CAT 2022 Slot 3

Nitu has an initial capital of Rs. $20,000$ . Out of this, she invests Rs. $8,000$ at $5.5\%$ in bank $A$ , Rs. $5,000$ at $5.6\%$ in bank $B$ and the remaining amount at $x \%$ in bank $C$ , each rate being simple interest per annum. Her combined annual interest income from these investments is equal to $5 \%$ of the initial capital. If she had invested her entire initial capital in back $C$ alone, then her annual interest income, in rupees, would have been

CAT 2024 Slot 1

An amount of Rs 10000 is deposited in bank A for a certain number of years at a simple interest of 5% per annum. On maturity, the total amount received is deposited in bank B for another 5 years at a simple interest of 6% per annum. If the interests received from bank A and bank B are in the ratio 10 : 13, then the investment period, in years, in bank A is

Solution

Related questions:

Keyboard Shortcuts

CAT Past Year Questions (Topic-Wise)