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Solved Examples(Set 7) - Simple Interest

31. A sum was put with simple interest at a certain rate for $2$ years. Had it been put at $4\%$ higher rate, it would have fetched $₹60$ more. What is the sum?
A. $₹940$B. $₹820$
C. $₹700$D. $₹750$
Discuss
answer with explanation

Answer: Option D

Explanation:

Solution 1

Let the sum be $x$ and the rate be $\text{R}\%$.

$\dfrac{x×(\text{R}+4)×2}{100}-\dfrac{x×\text{R}×2}{100}=60\\\Rightarrow \dfrac{x×4×2}{100}=60\\\Rightarrow x=750$

Solution 2

Let the sum be $x$

Simple interest on $x$ at $4\%$ is $60.$ Therefore,

$\dfrac{x×4×2}{100}=60\\\Rightarrow x=750$

Solution 3

Let the sum be $x$

$4\%\text{ for }2\text{ year }\implies 60\\100\%\text{ for }1\text{ year }\implies \dfrac{60×25}{2}=750$

Therefore, the sum is $₹750$

32. The simple interest on a sum at $x\%$ for $x$ years is $x.$ What is the sum?
A. $\dfrac{100}{x}$B. $\dfrac{100}{x^2}$
C. $x^2$D. $x$
Discuss
answer with explanation

Answer: Option A

Explanation:

$\text{P}=\dfrac{100×\text{SI}}{\text{RT}}=\dfrac{100×x}{x×x}=\dfrac{100}{x}$
33. A sum of money becomes $\dfrac{7}{5}$ of itself in $4$ years at a certain rate of simple interest. What is the rate of interest per annum?
A. $12\%$B. $11\%$
C. $9\%$D. $10\%$
Discuss
answer with explanation

Answer: Option D

Explanation:

Solution 1

Let the sum be $x$

Amount after $4$ years $=\dfrac{7x}{5}$
SI for $4$ years $=\dfrac{7x}{5}-x=\dfrac{2x}{5}$

$\text{R}=\dfrac{100×\text{SI}}{\text{PT}}=\dfrac{100×\dfrac{2x}{5} }{x×4}=10$

Solution 2

The sum makes $\dfrac{2}{5}$ of itself in $4$ years. That is$,40\%$ in $4$ years. That is $10\%$ each year.

Therefore, rate of interest per annum is $10\%$

34. If the simple interest on $₹2000$ is less than the simple interest on $₹3000$ at $5\%$ by $₹50,$ find the time.
A. $2$ yearsB. $1.5$ years
C. $2.5$ yearsD. $1$ year
Discuss
answer with explanation

Answer: Option D

Explanation:

Solution 1

$\dfrac{3000×5×\text{T}}{100}-\dfrac{2000×5×\text{T}}{100}=50\\\dfrac{(3000-2000)5\text{T}}{100}=50\\\text{T}=1$

Solution 2

Simple interest on $(3000-2000)$ at $5\%$ is $50$

$\text{T}=\dfrac{100×50}{1000×5}=1$

35. A sum of $₹7700$ is to be divided among three brothers Vikas, Vijay and Viraj in such a way that simple interest on each part at $5\%$ per annum after $1,2$ and $3$ years respectively remains equal. The Share of Vikas is more than that of Viraj by:
A. $₹2800$B. $₹1200$
C. $₹1400$D. $₹2200$
Discuss
answer with explanation

Answer: Option A

Explanation:

Solution 1

Let share of Vikas, Vijay and Viraj be $x,y$ and $z$ respectively.

Simple interest on $x$ at $5\%$ for $1$ year
= Simple interest on $y$ at $5\%$ for $2$ year
= Simple interest on $z$ at $5\%$ for $3$ year

$\dfrac{x×5×1}{100}=\dfrac{y×5×2}{100}=\dfrac{z×5×3}{100}\\\Rightarrow x=2y=3z\\\Rightarrow y=\dfrac{x}{2};\quad z=\dfrac{x}{3}~\cdots(1)$

$x+y+z=7700\\\Rightarrow x+\dfrac{x}{2}+\dfrac{x}{3}=7700 \quad \class{ct5}{[ \text{from(1)}]}\\\Rightarrow 11x=6×7700\\\Rightarrow x=4200$

$z=\dfrac{x}{3}=\dfrac{4200}{3}=1400$

That is, Vikas gets $₹4200$ and Viraj gets $₹1400$

Share of Vikas is more than that of Viraj by $(4200-1400)=2800$

Solution 2

Refer formula

Share of Vikas : Share of Vijay : Share of Viraj
$=\dfrac{1}{\text{R}_1\text{T}_1}:\dfrac{1}{\text{R}_2\text{T}_2} : \dfrac{1}{\text{R}_3\text{T}_3}\\=\dfrac{1}{\text{T}_1}:\dfrac{1}{\text{T}_2}:\dfrac{1}{\text{T}_3}~\class{ct5}{(\because \text{R}_1=\text{R}_2=\text{R}_3)}\\=\dfrac{1}{1}:\dfrac{1}{2}:\dfrac{1}{3}\\=6:3:2$

Total amount $=₹7700$

Share of Vikas - share of Viraj
$=\dfrac{7700(6-2)}{11}=2800$

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