Question

If the annual rate of simple interest increases from 11% to \(17 \frac 1 2\%\), a person's yearly income increases by Rs. 1,071.20. The principal amount invested (in Rs.) is:
1. 16,480
2. 19,120
3. 17,250
4. 10,710

Answer 1

Correct Answer - Option 1 : 16,480

Given:

Rate = 11%

Rate = \(17 \frac 1 2\%\)

Increase in Amount = Rs. 1,071.20

Formula used:

(i) SI = PRT/100

Where, P = principal

R = rate

T = time

(ii) A = SI + P

Where, A = Amount

SI = simple interest

Calculations:

A = SI + P

⇒ A = PRT/100 + P

⇒ A = P{(PRT/100) + 1}

For R = 11%

⇒ A₁ = P{(11/100) + 1}

For R = \(17 \frac 1 2\%\)

⇒ A₂ = P{(35/200) + 1}

A₂ - A₁ = P{(35/200) + 1} - P{(11/100) + 1}

⇒ P{35/200 + 1 - 11/100 - 1}

⇒ P{35/200 - 11/100}

⇒ P{(35 - 22)/200}

⇒ 13P/200 = 1,071.20

⇒ P = 214240/13

⇒ 16,480

∴ The principal amount invested is Rs.16,480.