A sum of money lent at S.I. amounts to Rs. 6,500 after 2 years and amo

1.	A sum of money lent at S.I. amounts to Rs. 6,500 after 2 years and amounts to Rs. 9,000 after 7 years at same rate of interest. What is the rate of interest per annum?1. 11% p.a.2. 9% p.a.3. 11.11% p.a.4. 9.09% p.a.
Answer» Correct Answer - Option 4 : 9.09% p.a. Given: A sum of money lent at S.I. amounts to Rs. 6,500 after 2 years and amounts to Rs. 9,000 after 7 years at same rate of interest Concepts used: S.I. = P × R × T/100 Where, P = Principal, R = Rate of interest per annum, T = Time (in years) Calculation: Amount after 2 years = Rs. 6500 Amount after 7 years = Rs. 9000 S.I of 5 years = Rs. (9000 – 6500) ⇒ Rs. 2500 S.I of 1 year = Rs. 2500/5 ⇒ Rs. 500 S.I of 2 years = Rs. (500 × 2) ⇒ Rs. 1000 Principal = Rs. (6500 – 1000) ⇒ Rs. 5500 Rate of interest = (500 × 100)/5500% ⇒ 100/11% ⇒ 9.09% ∴ The rate of interest is 9.09%

A sum of money lent at S.I. amounts to Rs. 6,500 after 2 years and amounts to Rs. 9,000 after 7 years at same rate of interest. What is the rate of interest per annum?1. 11% p.a.2. 9% p.a.3. 11.11% p.a.4. 9.09% p.a.

Answer» Correct Answer - Option 4 : 9.09% p.a.

Given:

A sum of money lent at S.I. amounts to Rs. 6,500 after 2 years and amounts to Rs. 9,000 after 7 years at same rate of interest

Concepts used:

S.I. = P × R × T/100

Where, P = Principal, R = Rate of interest per annum, T = Time (in years)

Calculation:

Amount after 2 years = Rs. 6500

Amount after 7 years = Rs. 9000

S.I of 5 years = Rs. (9000 – 6500)

⇒ Rs. 2500

S.I of 1 year = Rs. 2500/5

⇒ Rs. 500

S.I of 2 years = Rs. (500 × 2)

⇒ Rs. 1000

Principal = Rs. (6500 – 1000)

⇒ Rs. 5500

Rate of interest = (500 × 100)/5500%

⇒ 100/11%

⇒ 9.09%

∴ The rate of interest is 9.09%

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