Question

Sinchan and Rahul invested Rs. X and Rs. (X + 1200) respectively in two different schemes on simple interest. If Sinchan invested at 10% per annum and Rahul invested at 12% per annum, the difference in interest collected by them after two years is Rs. 600. Find the sum invested by Sinchan.
1. 6000
2. 7500
3. 8000
4. 6500
5. 7800

Answer 1

Correct Answer - Option 5 : 7800

Given:

The sum invested by Sinchan is X, at 10% per annum for 2 years

The sum invested by Rahul is Rs. (X + 1200) at 12% per annum for 2 years

The difference between the interest received by them is Rs. 600

Formula used:

S.I = PRT/100

Where S.I = Simple interest,  P = Principal, R = Rate, T = time

Calculation:

S.I received by Sinchan = (X × 10 × 2)/100

S.I received by Rahul = {(X + 1200) × 12 × 2}/100

Now, according to the question, we can say,

[{(X + 1200) × 12 × 2}/100] - [(X × 10 × 2)/100] = 600

⇒ (4/100)[(X + 1200) × 6 - 5X] = 600

⇒ (1/25)[6X - 5X + 7200] = 600

⇒ [X + 7200] = 600 × 25

⇒ X = 15000 - 7200 = 7800

∴ The sum invested by Sinchan is Rs. 7800.