Question

A sum of Rs 18,750 is left in will by a father to be
divided between two sons, whose present age is 12
and 14 years respectively, such that when they attain
maturity at 18, the amount (Principal + interest)
received by each at 5% S.l. will be the same. Find the
sum allotted at present to each son.​

Answer 1

Younger son will receive Rs 9000 and elder son will receive Rs 9750

Solution:

Given, A sum of Rs 18,750 is left in will by a father to be divided between two sons,  

Whose present age is 12 and 14 years respectively

Such that when they attain maturity at 18, the amount (Principal + interest) received by each at 5% S.l. will be the same.  

Now, let the sum of amount divided to elder son be Rs "n"

Then amount to younger son will be Rs (18750 - n)

$\text { S. I } =\frac{\text { amount } \times \text {rate} \times \text {time}}{100}$

$\text { So, for elder son S.I }=\frac{n \times 5 \times 4}{100}$

[ we took time = 4 years because elder son will 18 years in 4 years ]

$\text { For younger son S.l }=\frac{(18750-n) \times 5 \times 6}{100}$

[ time = 6 because younger son will be 18 in 6 years ]

Now, total amount received by both will be equal

Amount (principle + interest) received by elder son = amount (principle + interest) received by younger son

$n+\frac{n \times 5 \times 4}{100}=(18750-n)+\frac{(18750-n) \times 5 \times 6}{100}$

$\begin{array}{l}{n+\frac{20 n}{100}=(18750-n)+\frac{30(18750-n)}{100}} \\\\ {n+\frac{n}{5}=18750-n+\frac{3(18750-n)}{10}}\end{array}$

$\begin{array}{l}{10 n+2 n=10(18750-n)+3(18750-n)} \\\\ {12 n=13(18750-n)} \\\\ {12 n=13 \times 18750-13 n} \\\\ {12 n+13 n=13 \times 18750} \\\\ {25 n=13 \times 18750} \\\\ {n=13 \times 750} \\\\ {n=9750}\end{array}$

So, elder son will receive Rs 9750, then, younger son will receive 18750 – 9750 = 9000

Hence, younger son will receive Rs 9000 and elder son will receive Rs 9750