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Simple Interest #14

 14. A lent $₹5000$ to B for $2$ years and $₹3000$ to C for $4$ years on simple interest at the same rate of interest and received $₹2200$ in all from both of them as interest. What is the rate of interest per annum? A. $7\%$ B. $5\%$ C. $10\%$ D. $8\%$

Explanation:

Solution 1

Let required rate be R%

Simple interest on $₹5000$ for $2$ years + simple interest on $₹3000$ for $4$ years $=₹2200$

$\Rightarrow \dfrac{5000×\text{R}×2}{100}+\dfrac{3000×\text{R}×4}{100}=2200\\\Rightarrow \text{100R+120R}=2200\\\Rightarrow \text{220R}=2200\\\Rightarrow \text{R}=10$

Solution 2

SI on $₹5000$ for $2$ years + SI on $₹3000$ for $4$ years $=₹2200$
$\Rightarrow$ SI on $₹50$ for $1$ year + SI on $₹30$ for $2$ years $=₹11$
$\Rightarrow$ SI on $₹30$ for $\dfrac{5}{3}$ years + SI on $₹30$ on $2$ years $=₹11$
$\Rightarrow$ SI on $₹30$ for $\dfrac{11}{3}$ years $=₹11$
$\Rightarrow$ SI on $₹30$ for $1$ year $=₹3$
$\Rightarrow$ SI on $₹100$ for $1$ year $=₹10$

Therefore, required rate is $10\%$