Question

Assertion: When a certain sum is borrowed at compound interest, the interest paid is ₹ 215 more than if borrowed at simple interest for 2 years at 5% p.a, then the sum of money is ₹ 86,000.

Reason: CI - SI for 2 years = `P(r/100)^2`

Options

• Both A and R are true and R is the correct reason for A.

• Both A and R are true but R is the incorrect reason for A.

• A is true but R is false.

• A is false but R is true.

Answer 1

Both A and R are true and R is the correct reason for A.

Explanation:

Given:

• Difference between CI and SI for 2 years = ₹ 215 
• Rate of interest r = 5% p.a. 
• Time n = 2 years
• Find the principal P.

The reason given is the shortcut formula:

CI – SI for 2 years = `P(r/100)^2`

Step 1: Use the formula to find P

`CI - SI = P(r/100)^2`

Substitute the values:

`215 = P(5/100)^2`

`215 = P xx 25/(10,000)`

`215 = P xx 0.0025`

`P = 215/0.0025`

P = 86,000

The principal is ₹ 86,000, which matches the assertion.

Step 2: Check the reason

• Reason: CI – SI for 2 years = `P(r/100)^2`
• This is exactly the formula we used to calculate the sum.

Reason is true and it correctly explains the assertion.