A father left a will of Rs. 85,000 to be divided between his two sons aged 10 years and 12 years such that they may get equal amount when each attains the age of 18 years. If the money is invested at 10% p.a. simple interest, then find how much (in Rs.) would the son aged 10 years gets at the time of the execution of the will.1)  30,0002)  40,0003)  45,0004)  48,000

The problem is about simple interest and the time difference for each son to reach 18 years old.

The elder son is 12 years old, so he has 6 years until he turns 18. The younger son is 10 years old, so he has 8 years until he turns 18.

The father's will states that both sons should receive the same amount when they turn 18. This means that the money left to the younger son will earn interest for 2 more years than the money left to the elder son.

Let's denote the amount of money that the elder son receives as E and the amount that the younger son receives as Y.

We know that the total amount of money is Rs. 85,000, so we can write the equation:

E + Y = 85000 ...(1)

We also know that the money earns simple interest at a rate of 10% per year. So, after 6 years, the amount of money that the elder son receives will be E + 0.106E = E1.6. Similarly, after 8 years, the amount of money that the younger son receives will be Y + 0.108Y = Y1.8.

Since both amounts are supposed to be equal, we can write the equation:

1.6E = 1.8Y ...(2)

Now we can solve these two equations to find the values of E and Y.

From equation (2), we can express Y in terms of E: Y = 1.6E / 1.8 = 0.89E.

Substitute Y in equation (1): E + 0.89E = 85000, which simplifies to 1.89E = 85000. Solving for E gives E = 85000 / 1.89 = Rs. 44974.6.

So, the elder son would receive approximately Rs. 44974.6 at the time of the execution of the will.

Substitute E in equation (1) to find Y: Y = 85000 - 44974.6 = Rs. 40025.4.

So, the younger son (aged 10 years) would receive approximately Rs. 40025.4 at the time of the execution of the will.

Therefore, the closest answer is 2) Rs. 40,000.