Question

A man left rs18000,with the instruction that it should be devided among his three daughters aged 9,12, and 15 years in such a way that each should receive an equal amount when she reaches the age of 25 years.If the rate of interest be 7/2 % p.a compound,what should each daughter receive at her age of 25?​

Answer 1

Each Daughter Receive Rs 9350.5 at the age of 25

Step-by-step explanation:

Amount = 18000

Three daughters aged 9 , 12 & 15 years

15 year daughter will receive amount after 10 Years

12 Year Daughter will Receive amount after 13 Years

9 Year  Daughter will receive amount after 16 Years

Let say Each Daughter receive Amount = X

18000 will earn interest for 10 years

Amount after 10 Years = 18000 ( 1 + 3.5/100)¹⁰ = 25390.78

Now one Daughter will receive X

so Amount left = 25390.78 - X

Amount after next 3 years ( 13 Years) = (25390.78 - X) * (1.035)³

Now one Daughter will receive X

so Amount left =(25390.78 - X) * (1.035)³ - X

Amount after next 3 years ( 16 Years) = ((25390.78 - X) * (1.035)³ - X) * 1.035³ = X

X = 9350.5

Amount Received at age of 25 = Rs 9350.5

Another way

Amount divided = a , b & c

Amount received = a * 1.035¹⁶ =  b * 1.035¹³ = c*  1.035¹⁰

ac = b²

a + b + c = 18000

on solving we get

5392.5  , 5978.75 , 6628.75

Amount received = 9350.5