SSC GD Constable 5 Feb 2025 Shift 2 Paper

Section: Elementary Mathematics

Question : 48 of 80

Marks: +1, -0

Manoj has ₹1612 with him. He divided it amongst his sons Anand and Anil and asked them to invest it at 8% rate of interest compounded annually. It was seen that Anand and Anil got same amount after 13 and 14 years respectively. How much (in ₹) did Manoj give to Anand?

Validate

Solution:

{\Amount}(A)={\Principal}(P) ×(1+)^t

Calculation:
Let the amount given to Anand be ₹x.
Then, the amount given to Anil is ₹

(1612- x )

.
Amount received by Anand after 13 years

= x ×(1+)^{13}= x ×(1.08)^{13}

Amount received by Anil after 14 years

=(1612-x) ×(1+)^{14}=(1612-x) ×(1.08)^{14}

According to the question:

\;x ×(1.08)^{13}=(1612-x) ×(1.08)^{14}

\;⇒ x=(1612-x) ×(1.08)^{14} \/(1.08)^{13}

\;⇒ x=(1612-x) × 1.08

\;⇒ x=1612 × 1.08-1.08 x

\;⇒ x+1.08 x=1612 × 1.08

\;⇒ 2.08 x=1740.96

\;⇒ x=1740.96 \/ 2.08

\;⇒ x=837

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