Question

Divide ₹ 39030 between A and B so that when their shares are invested at 4% per annum compounded yearly, the amount that A receives in 5 years is same as B receives in 3 years.

Answer 1

Step 1: Set up the equations for the shares and the final amounts.

Let the share of A be P_A and the share of B be P_B.

The total sum is ₹ 39030.

So, P_A + P_B = 39030.

The formula for compound interest is A = P(1 + r)^t.

The interest rate is 4% = 0.04.

For A, the amount after 5 years (A_A) is:

A_A = P_A(1 + 0.04)⁵

A_A = P_A(1.04)⁵

For B, the amount after 3 years (A_B) is:

A_B = P_B(1 + 0.04)³

A_B = P_B(1.04)³

Step 2: Set the final amounts equal to each other.

According to the problem, the amounts A and B receive are the same:

A_A = A_B

P_A(1.04)⁵ = P_B(1.04)⁵

Step 3: Solve for the relationship between the shares.

Divide both sides by (1.04)³:

P_A(1.04)² = P_B

P_A(1.0816) = P_B

1.0816P_A = P_B

Step 4: Substitute and find the shares.

Substitute this relationship into the first equation from Step 1:

P_A + P_B = 39030

P_A + 1.0816P_A = 39030

2.0816P_A = 39030

`P_A = 39030/2.0816`

P_A = 18750

Now find P_B:

P_B = 39030 – P_A

P_B = 39030 – 18750

P_B = 20280

The shares of A and B are ₹ 18750 and ₹ 20280, respectively.