Question

The total sum of simple interest for 2 years at 10% and compound interest for 2 years at 8% on the same principal is Rs. 458. Then find the principal.
1. Rs. 1,425
2. Rs. 2,540
3. Rs. 1,250
4. Rs. 4,590
5. Rs. 2,500

Answer 1

Correct Answer - Option 3 : Rs. 1,250

Given:

The total sum of simple interest for 2 years at 10% and compound interest for 2 years at 8% on the same principal = Rs. 458

Concept used:

1.) S.I. = (P × T × R)/100

2.) C.I. = P(1 + R/100)^T – P

Where,

S.I. → Simple interest

C.I. → Compound interest

P → Principal

T → Time

R → Rate

Calculations:

Let the principal be x.

According to the question.

⇒ S.I. + C.I. = 458

⇒ (x × 2 × 10)/100 + [ x(1 + 8/100)² – x ] = 458

⇒ x/5 + 104x/625 = 458

⇒ 229x/625 = 458

⇒ x = (458 × 625)/229

⇒ x = Rs. 1,250

∴ The principal is Rs. 1,250