Arithmetic

Simple & Compound Interest

Medium

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 $250$ ?

$7250$

$7000$

$6350$

$6000$

✅ Correct Option: 1

We have three investors with different investment amounts and interest rates:

Investment ratio: Amala : Bina : Gouri = 3 : 4 : 5

Interest rate ratio: 6 : 5 : 4 (respectively)

Key condition: Bina's interest exceeds Amala's by Rs 250

When we have ratios, we represent them using a common factor. This makes calculations easier and helps us find the actual values.

Let's say the investments are:

Amala: $3x$

Bina: $4x$

Gouri: $5x$

To avoid fractions in interest calculations, let's multiply each investment by 100:

Amala: $300x$

Bina: $400x$

Gouri: $500x$

The interest rates are:

Amala: $6\%$ annually

Bina: $5\%$ annually

Gouri: $4\%$ annually

Simple Interest Formula: Interest = Principal × Rate × Time ÷ 100

Amala's interest income:

$= 300x \times 6 \times 1 \div 100$

$= 1800x \div 100$

$= 18x$

Bina's interest income:

$= 400x \times 5 \times 1 \div 100$

$= 2000x \div 100$

$= 20x$

Gouri's interest income:

$= 500x \times 4 \times 1 \div 100$

$= 2000x \div 100$

$= 20x$

Using the given condition:

Bina's interest income exceeds Amala's by Rs 250

This means: Bina's interest - Amala's interest = 250

$20x - 18x = 250$

$2x = 250$

$x = 125$

Now we can find each person's actual interest:

Amala's interest: $18x = 18 \times 125 = \text{Rs } 2250$

Bina's interest: $20x = 20 \times 125 = \text{Rs } 2500$

Gouri's interest: $20x = 20 \times 125 = \text{Rs } 2500$

Total interest income $= 18x + 20x + 20x = 58x = 58 \times 125 = \text{Rs } 7250$

Pattern Recognition: In ratio problems involving multiple variables, we express everything in terms of a single variable (like x), then use the given condition to solve for that variable. This approach works for any similar problem involving ratios and differences.

Answer: Rs 7250

CAT 2019 Slot 2

Amal invests Rs $12000$ at 8% interest, compounded annually, and Rs $10000$ at 6% interest, compounded semi-annually, both investments being for one year. Bimal invests his money at $7.5 \%$ simple interest for one year. If Amal and Bimal get the same amount of interest, then the amount, in Rupees, invested by Bimal is

CAT 2024 Slot 3

Aman invests Rs $4000$ in a bank at a certain rate of interest, compounded annually. If the ratio of the value of the investment after $3$ years to the value of the investment after $5$ years is $25: 36$ , then the minimum number of years required for the value of the investment to exceed Rs $20000$ is

CAT 2021 Slot 3

Bank $A$ offers $6 \%$ interest rate per annum compounded half yearly. Bank $B$ and Bank $C$ offer simple interest but the annual interest rate offered by Bank $C$ is twice that of Bank $B$ . Raju invests a certain amount in Bank B for a certain period and Rupa invests $₹ 10,000$ in Bank $C$ for twice that period. The interest that would accrue to Raju during that period is equal to the interest that would have accrued had he invested the same amount in Bank $A$ for one year. The interest accrued, in INR, to Rupa is

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 2018 Slot 2

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 $X+Y$ .

Amala, Bina, and Gouri invest money in the ratio 3:4:53: 4: 53:4:5 in fixed deposits having respective annual interest rates in the ratio 6:5:46: 5:46:5:4. What is their total interest income (in Rs) after a year, if Bina's interest income exceeds Amala's by Rs 250250250?

Solution

Related questions:

Keyboard Shortcuts

CAT Past Year Questions (Topic-Wise)

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 $250$ ?