Question

Sachin has two grandsons Chetan and Vipul. 13 year old Chetan gets some money from Sachin's wealth and 14 year old Vipul gets rest of the money. But Chetan and Vipul will get money only when they turn 23 years old. Till then the money is in a bank getting interest at rate 8% compounded annually. When both turn 23, they receive the same amount. How much had Sachin given Vipul (in ₹) initially, if total money with Sachin was ₹23400 ?

• A. 11000
• B. 12150
• C. 11250
• D. 12500

Answer 1

Answer:

B. 12150

Let the amounts given initially be:

• Chetan = ₹(x)

• Vipul = ₹(23400 - x)

  Time for investment

• Chetan (age 13 → 23): 10 years

• Vipul (age 14 → 23): 9 years

  Compound amount formula

$A = P(1 + r)^n$

Rate (r = 8% = 0.08)

Since both get equal amounts at age 23:
$x(1.08)^{10} = (23400 - x)(1.08)^9$
Simplify

Divide both sides by ((1.08)^9):
$x(1.08) = 23400 - x$
$1.08x + x = 23400$
$2.08x = 23400$
$x = \frac{23400}{2.08} = 11250$

So,

• Chetan = ₹11250

• $Vipul = (23400 - 11250 = 12150)$