SSC GD Constable 4 Feb 2025 Shift 1 Paper

Section: Elementary Mathematics

Question : 51 of 80

Marks: +1, -0

Mandar has two grandsons Ketan and Tushar. 11 year old Ketan gets some money from Mandar's wealth and 12 year old Tushar gets rest of the money. But Ketan and Tushar will get money only when they turn 22 years old. Till then the money is in a bank getting interest at rate 8% compounded annually. When both turn 22, they receive the same amount. How much had Mandar given Tushar (in ₹) initially, if total money with Mandar was ₹24700?

12825
11625
11875
13175

Validate

Solution:

{\Amount}( A )={\Principal}( P ) ×(1+ r \/ 100)^{ n }

Where n is the number of years.
Calculation:
Let Ketan's initial share be K and Tushar's initial share be T .

K+T=24700

Ketan's receiving time

=22-11=11

years
Tushar's receiving time

=22-12=10

years
Amount received by Ketan

= K ×(1+8 \/ 100)^{11}= K ×(1.08)^{11}

Amount received by Tushar

= T ×(1+8 \/ 100)^{10}= T ×(1.08)^{10}

Given that they receive the same amount:

\;⇒ K ×(1.08)^{11}=T ×(1.08)^{10}

\;⇒ K × 1.08=T

Substitute T in the first equation:

\;⇒ K+1.08 K=24700

\;⇒ 2.08 K=24700

\;⇒ K=24700 \/ 2.08

\;⇒ K=11875

Now find T:

\;T =24700- K

\;⇒ T =24700-11875

\;⇒ T=12825

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