Question

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?

• A. 6350
• B. 7250
• C. 7000
• D. 6000

Answer 1

The Correct Option is B

Let the investments be:

• Amala: \( 3x \)
• Bina: \( 4x \)
• Gouri: \( 5x \)

Let the corresponding annual interest rates be:

• Amala: \( 6y\% \)
• Bina: \( 5y\% \)
• Gouri: \( 4y\% \)

Step 1: Calculate Interest Incomes

• Amala's interest = \( \frac{3x \cdot 6y}{100} = \frac{18xy}{100} \)
• Bina's interest = \( \frac{4x \cdot 5y}{100} = \frac{20xy}{100} \)
• Gouri's interest = \( \frac{5x \cdot 4y}{100} = \frac{20xy}{100} \)

Step 2: Use Given Difference

Given: Bina's interest exceeds Amala's by ₹250

\[ \frac{20xy}{100} - \frac{18xy}{100} = 250 \Rightarrow \frac{2xy}{100} = 250 \Rightarrow 2xy = 25000 \Rightarrow xy = 12500 \]

Step 3: Total Interest Income

Total interest = \[ \frac{18xy + 20xy + 20xy}{100} = \frac{58xy}{100} \] Substitute \( xy = 12500 \): \[ \frac{58 \cdot 12500}{100} = 7250 \]

Final Answer:

\[ \boxed{₹7250} \]