Problem Solving

Alphonsaj wrote:A father left a will of $71 million between his 2 daughters aged 8.5 years and 12 years such that they may get equal amounts when each of them reach the age of 18 years. The father instructed that the original amount of 71mn be invested at 10% pa till such time the daughters turned 18. How much did the elder daughter get at the time of the will?

A.31mn
B.49mn
C.39mn
D.35.5mn
E.40mn

We can PLUG IN THE ANSWERS, which represent the initial amount bequeathed to the elder daughter.
Since the elder daughter earns interest for only 6 years (from age 12 to age 18), while the younger daughter earns interest for 9.5 years (from age 8.5 to age 18), the elder daughter earns LESS TOTAL INTEREST than the younger daughter.
Yet both daughters must receive the SAME AMOUNT at age 18.
Implication:
To compensate for earning LESS INTEREST than the younger daughter, the elder daughter must receive a GREATER INITIAL AMOUNT than the younger daughter.
Thus, the elder daughter must receive MORE THAN HALF of the $71 million.
Eliminate A and D.

Remaining options:
C) 39 million
E) 40 million
B) 49 million

Test the middle value.

Answer choice E: 40 million for the elder daughter, implying 31 million for the younger daughter
Elder daughter:
Yearly interest = 10% of 40 million = 4 million.
Total interest after 6 years = 6*4 = 24 million.
Amount received at 18 years = initial amount + interest = 40+24 = 64 million.

Younger daughter:
Yearly interest = 10% of 31 million = 3.1 million.
Total interest after 9.5 years = (9.5)(3.1) ⩳ 29 million.
Amount received at 18 years = initial amount + interest ⩳ 31+29 = 60 million.

Here, the elder daughter receives too much money at age 18.
Eliminate E.

For the elder daughter to receive LESS MONEY at age 18, she must receive a SMALLER INITIAL AMOUNT.

The correct answer is C.

Answer choice C: 39 million for the elder daughter, implying 32 million for the younger daughter
Elder daughter:
Yearly interest = 10% of 39 million = 3.9 million.
Total interest after 6 years = (6)(3.9) = 23.4 million.
Amount received at 18 years = initial amount + interest = 39 + 23.4 = 62.4 million.

Younger daughter:
Yearly interest = 10% of 32 million = 3.2 million.
Total interest after 9.5 years = (9.5)(3.2) ⩳ 30.4 million.
Amount received at 18 years = initial amount + interest ⩳ 32 + 30.4 = 62.4 million.
Success!