Question

dhruv invest money in two different schemes for 6 years and 9 years at 15% and 12% simple interest respectively​

Answer 1

Answer:

A person invests money in three different schemes for 6 years, 10 years and 12 years at 10%,12% and 15% simple interest respectively. At the completion of each scheme, he gets the same interest. What is the ratio of his investments?

Step-by-step explanation:

6:3:2

Answer 2

Q: Dhruv invests money in two different schemes for 6 years and 9 years at 15% and 12% simple interest respectively​. At the completion of each scheme, he gets the same interest. What is the ratio of his investments?

Tip: Recall the equation of simple interest

$I=\frac{PRT}{100}$, where $I=$simple interest, $P=$principal amount, $R=$rate of interest, $T=$time in years

Given:

The amount $P_1$ is invested for a simple interest of $15\%$ for $6$ years

The amount $P_2$ is invested for a simple interest of $12\%$ for $9$ years

Explanation:

Interest in the first scheme,

$I_1=\frac{P_1R_1T_1}{100} \\\implies I_1=\frac{P_1 \times 15 \times6}{100}$.............(1)

Interest in the second scheme,

$I_2=\frac{P_2R_2T_2}{100} \\\implies I_2=\frac{P_2 \times 12 \times9}{100}$.............(2)

Since the interest received is the same, equate (1) and (2)

$\implies \frac{P_1\times15\times6}{100} =\frac{P_2\times12\times9}{100} \\\\\implies P_1\times15\times6}=P_2\times12\times9} \\\\\implies \frac{P_1}{P_2} =\frac{12\times9}{15\times6} \\\\\implies \frac{P_1}{P_2} =\frac{6}{5}$

Hence the ratio of investment is $6:5$