Solved Examples(Set 7) - Simple Interest

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 $₹750$

Answer: Option A

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 $10\%$

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 $50$

$\text{T}=\dfrac{100×50}{1000×5}=1$

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
$=\dfrac{7700(6-2)}{11}=2800$