Question

A certain sum amounts to Rs. 12705 at 10% p. a. compounded interest after \(2\dfrac{1}{2}\) years, when the interest is compounded yearly. If the same sum amounts to Rs. 14500 at the same rate is x years at simple interest then the value of x is:
1. 5
2. \(4\dfrac{1}{2}\)
3. \(5\dfrac{1}{2}\)
4. 4

Answer 1

Correct Answer - Option 2 : \(4\dfrac{1}{2}\)

Given:

In first case:

Rate of interest (r) = 10% p.a.

Time (t) =  \(2\dfrac{1}{2}\)years 

Amount (A) = Rs. 12705

In second case:

Amount = Rs. 14500

Rate = 10%

Time = x years

Formula Used:

If a certain principal/sum be P, Rate of interest be r% and time be t year

Then, (A) = P(1 + r/100)t

SI = PRT/100

Where P = PrincipaL, R = Rate of interest, T = Time and SI = Simple interest

SI = A - P

Calculation:

In first case:

According to the question,

Let sum be Rs. P

12705 = P(1 + 10/100)^{\(2\dfrac{1}{2}\)}

⇒ 12705 = P(1 + 10/100)2 × (1 + 10/100)^{\(\dfrac{1}{2}\)}

⇒ 12705 = P × 121/100 × (1 + 10/2× 100)

⇒ 12705 = P × 121/100 × 21/20

⇒ P = 12705 × 100/121 × 20/21 = Rs. 10,000

Now,

In second case:

SI = 14500 - 10000 = Rs. 4500

SI = PRT/100

⇒ 4500 = (10000 × 10 × x)/100

⇒ x = 45/10 = \(4\dfrac{1}{2}\) years.

∴ The value of x is \(4\dfrac{1}{2}\) years.