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An amount becomes Rs. 10,000 in 4 years and Rs. 11000 in 6 years at simple interest. Find the rate of interest?
1. \(6\frac{1}{4}\)% p.a.
2. 6% p.a.
3. 6.5% p.a.
4. 7% p.a.

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Correct Answer - Option 1 : \(6\frac{1}{4}\)% p.a.

Given:

An amount becomes Rs. 10,000 in 4 years

The same amount becomes Rs. 11,000 in 6 years

Formula Used:

Simple interest = (Principal × Time × Rate of interest)/100

Simple interest =  Amount - Principal

Calculation:

The difference in the amount in 2 years (6 - 4) = Simple interest in 2 years

⇒ Rs. 11,000 -  Rs. 10,000  = Rs. 1,000

So, simple interest for 1 year = 1000/2 = Rs. 500

⇒ Simple interest for 4 years = 500 × 4 = Rs. 2000

Principal = Amount - Simple interest 

⇒ Principal =  Rs. 10,000 - Rs. 2,000 = Rs. 8,000

Rate of interest = (simple interest0 × 10)/(Principal × Time)

⇒ Rate of interest = (500 × 100)/(8000 × 1)

∴ Rate of interest = \(6\frac{1}{4}\)% p.a.

The correct option is 1 i.e. \(6\frac{1}{4}\)% p.a.

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