Question

Divide ₹ 8400 between A and B so that when their shares are invested at 10% compounded yearly, the amount that A receives in 4 years is the same as B receives in 5 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 ₹ 8400.

So, P_A + P_B = 8400.

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

For A, the amount received after 4 years (A_A) is:

A_A = P_A(1 + 0.10)⁴

A_A = P_A(1.1)⁴

For B, the amount received after 5 years (A_B) is :

A_B = P_B(1 + 0.10)⁵

A_B = P_B(1.1)⁵

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(1.1)⁴ = P_B(1.1)⁵

Step 3: Solve for the relationship between the shares.

Divide both sides by (1.1)⁴:

P_A = P_B(1.1)

P_A = 1.1 × P_B

Step 4: Substitute and find the shares.

Substitute this relationship into the first equation from Step 1:

P_A + P_B = 8400

(1.1 × P_B) + P_B = 8400

2.1 × P_B = 8400

`P_B = 8400/2.1`

P_B = 4000

Now find P_A:

P_A = 8400 – P_B

P_A = 8400 – 4000

P_A = 4400

The shares of A and B are ₹ 4400 and ₹ 4000, respectively.