Question

A sum of ₹69,300 is to be divided between two friends Michel and Vivian. They are 11 and 12 years old respectively. Their respective portions are compounded annually at 10% per annum. If they get the same amount when they are 24 years old, what is the share of Vivian?

• A. ₹ 36,300
• B. ₹ 33,000
• C. ₹ 34,000
• D. ₹ 35,300

Answer 1

The correct option is A ₹ 36,300

Let the share of Michel be ₹x.

Share of Vivian = ₹(69,300- x)

Time period for Vivian = final age – initial age = 24 – 12 = 12 years
Time period for Michel = final age – initial age = 24 – 11 = 13 years

Amount received by Michel after 13 years = $P(1+\frac{R}{100}{)}^n$ = $x(1+\frac{10}{100}{)}^{13}$

And, the amount received by Vivian after 12 years = $P(1+\frac{R}{100}{)}^n$

= $(69,300-x)(1+\frac{10}{100}{)}^{12}$

As per the question, both of them will get the same amount of money when they are 24 years old.

So, $x(1+\frac{10}{100}{)}^{13}=(69,300-x\left)\right(1+\frac{10}{100}{)}^{12}$

$\Rightarrow$ $x\left(\frac{110}{100}\right)$ = $69,300-x$
$110x=100(69,300-x)$
$110x+100x=6,93,00,00$
$x=33,000$
So, share of Michel = $₹33,000$
Share of Vivian = $₹(69,300-33,000)$ = $₹36,300$