Rinku invested ₹X in scheme A for 3 years at 15% rate of simple interest and ₹Y in scheme B for 2 years at 20% compound rate of interest. If the value of X is ₹400 less than the value of Y and the amount of interest from scheme A is ₹164 less than that received from scheme B, then what is the ratio of the value of X to the value of Y?
Question
Rinku invested ₹X in scheme A for 3 years at 15% rate of simple interest and ₹Y in scheme B for 2 years at 20% compound rate of interest. If the value of X is ₹400 less than the value of Y and the amount of interest from scheme A is ₹164 less than that received from scheme B, then what is the ratio of the value of X to the value of Y?
Solution
To solve this problem, we need to use the formulas for simple interest and compound interest and the given conditions in the problem.
- Simple Interest (SI) = (Principal (P) * Rate (R) * Time (T)) / 100
- Compound Interest (CI) = P * (1 + R/100) ^ T - P
Given that Rinku invested ₹X in scheme A for 3 years at 15% rate of simple interest, the interest from scheme A (SI_A) can be calculated as:
SI_A = (X * 15 * 3) / 100 = 0.45X
Rinku invested ₹Y in scheme B for 2 years at 20% compound rate of interest. The interest from scheme B (CI_B) can be calculated as:
CI_B = Y * (1 + 20/100) ^ 2 - Y = 0.44Y
According to the problem, X is ₹400 less than Y and the amount of interest from scheme A is ₹164 less than that received from scheme B. So we have two equations:
X = Y - 400 0.45X = 0.44Y - 164
Substitute X in the second equation with Y - 400, we get:
0.45(Y - 400) = 0.44Y - 164 0.45Y - 180 = 0.44Y - 164 0.01Y = 16 Y = 16 / 0.01 = 1600
Substitute Y = 1600 into X = Y - 400, we get X = 1200.
Therefore, the ratio of the value of X to the value of Y is 1200 : 1600 = 3 : 4.
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