Question

The rates of simple interest in two banks A and B are in the ratio 5 : 4. A person wants to deposit his total savings in the two banks in such a way that he receives equal half yearly interest from both. He should deposit his savings in banks A and B in the ratio:
1. 5 : 2
2. 2 : 5
3. 4 : 5
4. 5 : 4

Answer 1

Correct Answer - Option 3 : 4 : 5

Given:

Ratio of the rates of Simple Interests in two banks A and B = 5 : 4

Half-yearly interests from both the banks are equal.

Formula Used:

Simple Interest (SI) = (P × R × T)/100;

where P = principal, R = Rate of Interest, T = Time period.

Calculation:

Let the principal amounts invested in banks A and B be A and B, respectively.

Let the respective rates of simple interest for banks A and B be 5x and 4x

Using the formula for SI, we get:

SI for bank A = (A × 5x × 0.5)/100 

Also, SI for bank B = (B × 4x × 0.5)/100 

Since the SI is the same for both the banks, we get:

(A × 5x × 0.5)/100 = (B × 4x × 0.5)/100 

⇒ 2.5A = 2B

⇒ A/B = 4/5

∴ The ratio in which deposit should be made in the banks A and B should be 4 : 5