A father left a will of Rs.35 lakhs between his two daughters aged 8.5 and 16 such that they may get equal amounts when they reach 21 years. The original amount was 35 lakhs at 10%. How much did the elder daughter get?
Question
A father left a will of Rs.35 lakhs between his two daughters aged 8.5 and 16 such that they may get equal amounts when they reach 21 years. The original amount was 35 lakhs at 10%. How much did the elder daughter get?
Solution
The elder daughter is 16 years old and she will reach 21 in 5 years. The younger daughter is 8.5 years old and she will reach 21 in 12.5 years.
The father left a will of Rs.35 lakhs to be divided between his two daughters such that they may get equal amounts when they reach 21 years. This means the money left for them will be invested at a certain interest rate (10% per annum) and they will receive the final amount when they turn 21.
The elder daughter's share will accumulate interest for 5 years and the younger daughter's share will accumulate interest for 12.5 years. Since they are supposed to get equal amounts when they reach 21, we can set up the following equation using the formula for compound interest:
P1*(1 + 10/100)^5 = P2*(1 + 10/100)^12.5
Where P1 is the principal amount for the elder daughter and P2 is the principal amount for the younger daughter.
Solving this equation will give us the ratio of P1 to P2.
(1 + 10/100)^5 / (1 + 10/100)^12.5 = P1/P2
Calculating the above expression gives us approximately 0.44.
This means that the ratio of the elder daughter's share to the younger daughter's share is 0.44.
Since the total amount is Rs.35 lakhs, we can divide this amount in the ratio 0.44 to get the shares of the two daughters.
The elder daughter's share is 0.44 / (1 + 0.44) * 35 lakhs = Rs.14 lakhs approximately.
So, the elder daughter got Rs.14 lakhs.
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