SSC GD Constable 6 Feb 2025 Shift 1 Paper

Section: Elementary Mathematics

Question : 42 of 80

Marks: +1, -0

Ashish has ₹1617 with him. He divided it amongst his sons Arun and Mahesh and asked them to invest it at 10% rate of interest compounded annually. It was seen that Arun and Mahesh got same amount after 14 and 15 years respectively. How much (in ₹) did Ashish give to Arun?

Validate

Solution:

A=P(1+r \/ 100)^t

Where:
-

A =

Final amount
-

P =

Principal amount
-

t=

Time in years
-

r =

Rate of interest
Calculations:
Let the amount given to Arun

=₹ P_{\;\text "Arun "\;}

and to Mahesh

=₹ P_{\;\text "Mahesh "\;}

.
It is given that the final amounts are the same after respective times.

\;⇒ P_{\;\text "Arun "\;}(1+10 \/ 100)^{14}=P_{\;\text "Mahesh "\;}(1+10 \/ 100)^{15}

\;⇒ P_{\;\text "Arun "\;}(1.1)^{14}=P_{\;\text "Mahesh "\;}(1.1)^{15}

\;⇒ P_{\;\text "Arun "\;}=P_{\;\text "Mahesh "\;} ×(1.1)

Total amount distributed:

\;P_{\;\text "Arun "\;}+P_{\;\text "Mahesh "\;}=₹ 1617

\;\;\text " Substitute "\; P_{\;\text "Arun "\;}=P_{\;\text "Mahesh "\;} × 1.1:

\;⇒ P_{\;\text "Mahesh "\;} × 1.1+P_{\;\text "Mahesh "\;}=₹ 1617

\;⇒ P_{\;\text "Mahesh "\;}(1.1+1)=₹ 1617

\;⇒ P_{\;\text "Mahesh "\;}(2.1)=₹ 1617

\;⇒ P_{\;\text "Mahesh "\;}=₹ 1617 \/ 2.1

\;⇒ P_{\;\text "Mahesh "\;}=₹ 770

Now, calculate

P _{\;\text "Arun: "\;}

\;⇒ P_{\;\text "Arun "\;}=P_{\;\text "Mahesh "\;} × 1.1

\;⇒ P_{\;\text "Arun "\;}=₹ 770 × 1.1

\;⇒ P_{\;\text "Arun "\;}=₹ 847

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