SSC CHSL 12 Aug 2021 Shift 3 Paper

Section: Quantitative Aptitude

Question : 53 of 99

Marks: +1, -0

A man invests an amount of

₹ 105750

at simple interest in the name of his son, daughter and his wife in such a way that they get the same interest after 3,4 and

5 {yr}

, respectively. If the rate of interest is

5 \%

per annum, then the amount invested for the wife is

Solution:

Let the amount invested for wife and daughter be

₹ x

and

₹ y

, respectively.

∴

Amount invested for son

=₹[105750-(x+y)]

We know that,

{Sl}=\;{\;\text " Prt "\;}/{100}

According to the question,

\;{[105750-(x+y)] × 5 × 3}/{100}

\;\; =\;{y × 5 × 4}/{100}=\;{x × 5 × 5}/{100}

when,

\;{y × 5 × 4}/{100}=\;{x × 5 × 5}/{100}

⇒ \;\; y=\;{5}/{4} \;\text " of "\; x

. . . (i)
Now,

\;{[105750-(x+y)] × 5 × 3}/{100}=\;{x × 5 × 5}/{100}

⇒[105750-(x+\;{5 x}/{4})]

\;\; =\;{5 x}/{3} \;\; \;\text " [from Eq. (i) "\;]

⇒ \;\; \;{9 x}/{4}+\;{5 x}/{3}=105750

⇒ \;{27 x+20 x}/{12}=105750

⇒ \;\; \;{47 x}/{12}=105750

∴ \;\; x=\;{105750 × 12}/{47}=₹ 27000

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