The rates of simple interest in two banks. A and B are in the ratio 5 ...
Let the savings in the banks A and B be x and y respectively
∴ According to the given conditions,
⇒ (x × 0.5 × r1) = (y × 0.5 × r2)
∴xy=r2r1=45∴xy=r2r1=45
∴ The person should invest amounts in the ratio of 4 ∶ 5 in the banks A and B respectively
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The rates of simple interest in two banks. A and B are in the ratio 5 ...
Given:
- The rates of simple interest in two banks, A and B, are in the ratio 5 : 4.
To find:
- The ratio in which the person should deposit his savings in banks A and B in order to receive equal half-yearly interest from both.
Solution:
Let's assume that the person has a total savings of S.
Let the rate of interest in bank A be 5x and the rate of interest in bank B be 4x.
Calculating the interest:
For half-yearly interest, we need to divide the annual interest rate by 2.
The interest received from bank A after 6 months would be (S * 5x * (1/2)) = S * (5/2) * x.
The interest received from bank B after 6 months would be (S * 4x * (1/2)) = S * 2x.
Setting up the equation:
Since we want the person to receive equal half-yearly interest from both banks, we can equate the two expressions for the interest:
S * (5/2) * x = S * 2x.
Simplifying the equation:
Canceling out the common factors, we get:
(5/2) * x = 2x.
Solving for x:
Dividing both sides by x:
(5/2) = 2.
Cross multiplying:
2 * 5 = 2 * 2,
10 = 4.
Conclusion:
Since the equation does not hold true, we can conclude that our assumption that the rates of interest in banks A and B are in the ratio 5 : 4 is incorrect.
Therefore, the correct ratio in which the person should deposit his savings in banks A and B cannot be determined with the given information.
Hence, none of the provided options (a), b), c), or d)) is the correct answer.
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