A certain sum of money amounts to ₹ 9766 in 3 {yr} at simple interest at R \% per annum and to ₹ 10849 in 4 \frac{1}{2} {yr} at the same rate of simple interest. The value of R is

SSC CHSL 11 Aug 2021 Shift 2 Paper

Section: Quantitative Aptitude

Question : 70 of 100

Marks: +1, -0

A certain sum of money amounts to

₹ 9766

3 {yr}

at simple interest at

R \%

per annum and to

₹ 10849

4 \;{1}/{2} {yr}

at the same rate of simple interest. The value of

R

Solution:

Let the principal be

₹ x

.
According to the question,

\;{(9766-x) × 100}/{x × 3}=\;{(10849-x) × 100}/{x × \;{9}/{2}}

⇒ 3 × 9766-3 x=2 × 10849-2 x

⇒ 3 x-2 x=29298-21698

⇒ x=₹ 7600

∴ \;\text " SI of "\; 3 {yr}=9766-7600=₹ 2166

∴ \;\text " Rate of interest "\;

\;\;\; =\;{\;\text " SI "\; × 100}/{\;\text " Principal "\; × \;\text " Time "\;}

\;\;\; =\;{2166 × 100}/{7600 × 3}=9.5 \%

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