Question

a person invested money in two different schemes for 5 years and 8 years at 12% and 10% simple intrest respectively,at the completion of each scheme,the person gets the same intrest.what is the ratio of the person's investments?​

Answer 1

Given:

a person invested money in two different schemes for 5 years and 8 years at 12% and 10% simple interest respectively, at the completion of each scheme, the person gets the same interest.

To find:

What is the ratio of the person's investments?​

Solution:

We know,

$\boxed{\bold{Simple \:Interest = \frac{P \times R \times T}{100} }}$

For the 1st scheme:

Let "P₁" be the person's investment for the 1st scheme.

The rate of interest, R = 12%

The no. of years, T = 5 years

∴ $S.I._1 = \frac{P_1 \times 12\times 5}{100}$ . . . . (1)

For the 2nd scheme:

Let "P₂" be the person's investment for the 2nd scheme.

The rate of interest, R = 10%

The no. of years, T = 8 years

∴ $S.I._2 = \frac{P_2 \times 10\times 8}{100}$ . . . . (2)

Since the person gets the same interest at the end of each scheme, therefore, we can say

$S.I._1 = S.I._2$

on substituting from (1) and (2), we get

$\implies \frac{P_1 \times 12\times 5}{100}= \frac{P_2 \times 10\times 8}{100}$

$\implies P_1 \times 12\times 5=P_2 \times 10\times 8$

$\implies \frac{P_1 }{P_2} =\frac{10\times 8}{12\times 5}$

$\implies \bold{\frac{P_1 }{P_2} =\frac{4}{3}}$

Thus, the ratio of the person's investments is → $\underline{\bold{4:3 }}$.

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