Question

Mandar has two grandsons Ketan and Tushar. 11 years old Ketan gets some money From Mandar's wealth and 12 year old Tushar gets the rest of the money.But Ketan and Tushar will get the money only when they tunrs 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 INR) initially, If total money with Mandar was INR 24700?

• A. 11625
• B. 13175
• C. 12825
• D. 11875

Answer 1

Answer:

C. 12825

Let the initial amount given to Ketan = ₹K
Then the initial amount given to Tushar = ₹T

• Ketan’s age = 11 → money grows for 11 years

• Tushar’s age = 12 → money grows for 10 years

• Rate of interest = 8% p.a., compounded annually

• Total money = ₹24700

• Final amounts received at age 22 are equal

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$K(1.08)^{11} = T(1.08)^{10}$

Divide both sides by $((1.08)^{10}):$
$K(1.08) = T$
$T = 1.08K$
$K + T = 24700$
$K + 1.08K = 24700$
$2.08K = 24700$
$K = 11875$

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$T = 1.08 \times 11875 = 12825$

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Mandar had initially given ₹12,825 to Tushar.