Question

Raj has ₹1612 with him. He divided it amongst his sons Varun and Ashish and asked them to invest it at 8% rate of interest compounded annually. It was seen that Varun and Ashish got same amount after 18 and 19 years respectively. How much (in ₹) did Raj give to Varun ?

• A. 875
• B. 775
• C. 837
• D. 687

Answer 1

Answer:

C. 837

Let the amount given to Varun = ₹x
Then amount given to Ashish = ₹(1612 − x)

Given:

• Rate = 8% = 1.08

• Compounded annually

• Varun invests for 18 years, Ashish for 19 years

• Final amounts are equal

So,

$x(1.08)^{18} = (1612 - x)(1.08)^{19}$

Divide both sides by ((1.08)^{18}):

$x = (1612 - x)(1.08)$

Now solve:
$x = 1.08 \times 1612 - 1.08x$
$x + 1.08x = 1.08 \times 1612$
$2.08x = 1.08 \times 1612$
$x = \frac{1.08}{2.08} \times 1612$
$\frac{1.08}{2.08} = \frac{108}{208} = \frac{27}{52}$
$x = 1612 \times \frac{27}{52}$
$x = 31 \times 27 = 837$
Raj gave ₹837 to Varun