Question

A sum of money amounts to Rs. 10,400 in 6 years and Rs.11,200 in 8 years. Find the sum and rate of interest.​

Answer 1

Note: This problem claims to be of simple interest. If P be the sum, t be the time of investment, r% be the rate of simple interest and I be the interest after r years, then

I = Ptr / 100

Solution:

Let, P be the sum and r be the rate of simple interest.

Step 1.

After 6 years, the interest of P in r% rate be

= Rs. (P * 6 * r) / 100

= Rs. (6Pr / 100)

Money amounted after 6 years

= Rs. (P + 6Pr/100)

ATQ, P + 6Pr/100 = 10400 ..... (1)

Step 2.

After 8 years, the interest of P in r% rate be

= Rs. (P * 8 * r) / 100

= Rs. (8Pr / 100)

Money amounted after 8 years

= Rs. (P + 8Pr/100)

ATQ, P + 8Pr/100 = 11200 ..... (2)

Step 3.

Subtracting (1) from (2), we get

2Pr/100 = 800

or, Pr = 40000 ..... (3)

From (1), we get

P + 6Pr/100 = 10400

or, P + (6 * 40000)/100 = 10400

or, P = 10400 - 2400

or, P = 8000

From (3), we get

Pr = 40000

or, r = 40000 / 8000

or, r = 5

Therefore, the sum is Rs. 8000 and the rate of interest (simple) is 5%

i have a fracture so please ignore if there are some mistakes