Question

A certain sum amounts to Rs. 22,494 in 7 years at x% per annum on simple interest. If the rate of simple interest per annum had been (x + 4)%, the amount payable after 7 years would have been Rs. 25,917. Find the sum invested.

• A. Rs. 11,975
• B. Rs. 12,275
• C. Rs. 12,175
• D. Rs. 12,225

Answer 1

Answer:

D. Rs. 12,225

Solution:

Given:

Rate of interest for 1st case = x%

Rate of interest for 2nd case = (x + 4)%

Time = 7 years

Concept used:

S.I = PTR/100

Amount = SI + P

Here

P = principal or sum

T = time

R = rate of interest

Calculation:

Let sum be 100a

Now,

$100a+\rm\frac{100a × (x+4)×7}{100}=Rs.25917$

⇒ 100a + 7xa = Rs. 22494      ----(i)

Again,

$100a+\rm\frac{100a × (x+4)×7}{100}=Rs.25917$

⇒ 100a + 7xa + 28a = Rs. 25917      ----(ii)

Putting the value of eq (i) in eq (ii) we get

22494 + 28a = 25917

⇒ 28a = 3423

⇒ a = 122.25

So, 100a = 12225 i.e the sum

∴ The sum invested is Rs. 12225.