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CAT 2022 Slot 1 — QA Question 21

Simple InterestEasy

Alex invested his savings in two parts. The simple interest earned on the first part at 15% per annum for 4 years is the same as the simple interest earned on the second part at 12% per annum for 3 years. Then, the percentage of his savings invested in the first part is

Answer & solution

  • A

    40%

  • B

    62.5%

  • C

    60%

  • 37.5%

Solution

Easy

Equal simple interest means equal P×R×TP\times R\times T products. Set the two SI expressions equal to get the ratio F:SF:S, then express the first part as a percentage of the whole.

1

Equate the two simple interests (FF = first part, SS = second part):

F×15×4100=S×12×3100⇒ 60F=36S\begin{aligned} &\frac{F\times 15\times 4}{100}=\frac{S\times 12\times 3}{100}\\ &\Rightarrow\ 60F=36S \end{aligned}
2

Get the ratio:

FS=3660=35⇒ F:S=3:5\begin{aligned} &\frac{F}{S}=\frac{36}{60}=\frac{3}{5}\\ &\Rightarrow\ F:S=3:5 \end{aligned}
3

First part as a percentage of total savings F+S=3+5=8F+S=3+5=8 parts:

33+5×100%=38×100%=37.5%\begin{aligned} &\frac{3}{3+5}\times 100\%=\frac{3}{8}\times 100\%=37.5\% \end{aligned}

First part =37.5%=\mathbf{37.5\%} of savings. Option (d).

SI is proportional to R×TR\times T. First part has 15×4=6015\times4=60, second has 12×3=3612\times3=36. For equal interest, principals go in the inverse ratio 36:60=3:536:60=3:5, so the first part is 38=37.5%\frac{3}{8}=37.5\%.

CAT 2022 Slot 1 QA Q21: Alex invested his savings in two parts. The simple interest earned on the first part at 15% per annum for 4 ye — Solution | TheCATExam