If the ratio of the difference between compound interest and Simple In

1.	If the ratio of the difference between compound interest and Simple Interest for 3 years and 2 years is 31 ∶ 10, then find the Rate of Interest.1. 11.11%2. 10%3. 20%4. 25%5. None of these
Answer» Correct Answer - Option 2 : 10% Given: Difference between C.I. and S.I. for 3 years : Difference between C.I. and S.I. for 2 years = 31 : 10 Formula used: Difference between C.I. and S.I. for 3 years = P(R/100)²(300 + R)/100 Difference between C.I. and S.I. for 2 years = P(R/100)² Calculations: Difference between C.I. and S.I. for 3 years : Difference between C.I. and S.I. for 2 years = 31 : 10 \(\Rightarrow \;\frac{{P{{\left( {\frac{R}{{100}}} \right)}^2}\left( {\frac{{300\; + \;R}}{{100}}} \right)\;}}{{P{{\left( {\frac{R}{{100}}} \right)}^2}}}\; = \;\frac{{31}}{{10}}\) ⇒ (300 + R)/100 = 31/10 ⇒ 3000 + 10R = 3100 ⇒ 10R = 100 ⇒ R = 10% ∴ The required rate is 10%

If the ratio of the difference between compound interest and Simple Interest for 3 years and 2 years is 31 ∶ 10, then find the Rate of Interest.1. 11.11%2. 10%3. 20%4. 25%5. None of these

Answer» Correct Answer - Option 2 : 10%

Given:

Difference between C.I. and S.I. for 3 years : Difference between C.I. and S.I. for 2 years = 31 : 10

Formula used:

Difference between C.I. and S.I. for 3 years = P(R/100)²(300 + R)/100

Difference between C.I. and S.I. for 2 years = P(R/100)²

Calculations:

Difference between C.I. and S.I. for 3 years : Difference between C.I. and S.I. for 2 years = 31 : 10

\(\Rightarrow \;\frac{{P{{\left( {\frac{R}{{100}}} \right)}^2}\left( {\frac{{300\; + \;R}}{{100}}} \right)\;}}{{P{{\left( {\frac{R}{{100}}} \right)}^2}}}\; = \;\frac{{31}}{{10}}\)

⇒ (300 + R)/100 = 31/10

⇒ 3000 + 10R = 3100

⇒ 10R = 100

⇒ R = 10%

∴ The required rate is 10%

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