Question

Mohan invested a sum of the amount at the rate of 15% SI per annum for two years and received a total amount of Rs.9984. He invested the same amount at the rate x% per annum at CI for two years and he received interest Rs. 6500 more as compared to the Simple Interest, then find the value of x%.(approximately.)

1. 46.5%
2. 30.5%
3. 25.5%
4. 35.5%
5. 22.5%

Answer 1

Correct Answer - Option 1 : 46.5%

Given:

The amount received = Rs. 9984

Formula used:

SI = (P × R × T)/100

Total amount = P(1 + x/100)^t

Calculation:

Let the Sum be the x

⇒ 130/100 × x = 9984

⇒ x = (9984 × 100)/130

⇒ x =  Rs. 7680

SI = (P × R × T)/100

S.I = (7680 × 15 × 2)/100

⇒ S.I = Rs. 2304

According to question

C.I = 2304 + 6500

⇒  Rs. 8804

Total amount = 7680 + 8804

Total amount = P(1 + x/100)t

⇒ 16484 = 7680(1 + x/100)²

⇒ (1 + x/100)2  = 16484/7680

⇒ 1 + x/100 = √2.1463 

⇒ x/100 = 1.465 – 1

⇒ x = 46.5%

∴ The value of x is 46.5%