A father leaves a will of Rs. 35 lakhs to be divided between his two daughters aged 8.5 years and 16 years so that each will receive an equal amount when she reaches 21 years. The amount is to be invested at 10% per annum simple interest until each daughter turns 21. What amount (in lakhs of rupees) is given to the elder daughter at the time of the will?

Introduction / Context:This is an application of simple interest to a real life style situation involving a will and future equalization of amounts. The core idea is that the younger daughter's share will earn interest for a longer period, so she must receive a smaller initial amount than the elder daughter in order for both to end up with the same final amount at age 21.Given Data / Assumptions:

• Total amount in the will = Rs. 35 lakhs
• Age of elder daughter = 16 years
• Age of younger daughter = 8.5 years
• Both sums are invested at 10% per annum simple interest
• Each daughter receives her amount when she turns 21 years
• Let A be the amount initially given to the elder daughter and B be the amount given to the younger daughter

Concept / Approach:The time for which the elder daughter's amount is invested is 21 - 16 = 5 years. For the younger daughter, the time is 21 - 8.5 = 12.5 years. At simple interest, the amount after time T at rate R is:Final amount = Principal * (1 + (R * T) / 100)We require that both daughters get equal final amounts at age 21 and also that A + B = 35 lakhs.Step-by-Step Solution:Time for elder daughter = 5 yearsTime for younger daughter = 12.5 yearsRate = 10% per annumFinal amount for elder daughter = A * (1 + (10 * 5) / 100) = A * (1 + 0.5) = 1.5AFinal amount for younger daughter = B * (1 + (10 * 12.5) / 100) = B * (1 + 1.25) = 2.25BSince they must be equal: 1.5A = 2.25BDivide both sides by 0.75: 2A = 3B, so B = (2A) / 3Also A + B = 35So A + (2A) / 3 = 35(5A) / 3 = 35A = (35 * 3) / 5 = 21Therefore, the elder daughter gets 21 lakhs and the younger gets 35 - 21 = 14 lakhsVerification / Alternative check:Check final equal amounts. Elder daughter: after 5 years at 10%, amount = 21 * (1 + 0.5) = 21 * 1.5 = 31.5 lakhs. Younger daughter: after 12.5 years at 10%, amount = 14 * (1 + 1.25) = 14 * 2.25 = 31.5 lakhs. Both final amounts match, so the division is correct.Why Other Options Are Wrong:If the elder daughter received 17.5, 15 or 20 lakhs, the resulting final amounts at age 21 would not be equal for both daughters, once the simple interest over the different time periods is considered. Only 21 lakhs for the elder daughter leads to equal final amounts that also sum to 35 lakhs initially.Common Pitfalls:Some students mistakenly try to divide the original amount proportionally to the times without setting up the correct equations for simple interest. Others forget to convert 8.5 into 12.5 years of remaining time. Always express the conditions as equations for the final amounts and solve systematically.Final Answer:The elder daughter receives Rs. 21 lakhs at the time of the will.