Question

An article was sold at a profit of 12%. If the cost price would be 10% less and selling price would be Rs.5.75 more, there would be a profit of 30%. Then at what price it should be sold to make a profit of 20% ?

Answer 1

Answer :

Let Cost price = x
As given : An article was sold at a profit of 12%
So,
Selling price = x + 12% of x = x + $\frac{12x}{100}=x+\frac{3x}{25}=\frac{25x+3x}{25}=\frac{\mathbf{28}\mathbf{x}}{\mathbf{25}}$
And as given : the cost price would be 10% less
So,
New cost price = x - 10% of x = x - $\frac{10x}{100}=x-\frac{x}{10}=\frac{10x-x}{10}=\frac{\mathbf{9}\mathbf{x}}{\mathbf{10}}$
And , selling price would be Rs.5.75 more
So,
New selling price = $\frac{28\mathrm{x}}{25}+5.75=\frac{28x+143.75}{25}$
And now profit will be 30% , So we get

$$\begin{gathered} \frac{\frac{28x+143.75}{25}-\frac{9x}{10}}{\frac{9x}{10}}\times 100=30 \\ \Rightarrow \frac{\frac{56x+287.50-45x}{50}}{\frac{9x}{10}}\times 100=30 \\ \Rightarrow \frac{\frac{11x+287.50}{50}}{\frac{9x}{10}}\times 100=30 \\ \Rightarrow \frac{\left(11x+287.50\right)10}{50\times 9x}\times 100=30 \\ \Rightarrow \frac{\left(11x+287.50\right)10}{9x}\times 2=30 \\ \Rightarrow \frac{\left(11x+287.50\right)20}{9x}=30 \\ \Rightarrow 220x+\hspace{0.17em}5750=270x \\ \Rightarrow 50x=5750 \\ \Rightarrow x=\frac{5750}{50} \\ \Rightarrow x=115 \end{gathered}$$
So,

price of article should be sold to make a profit of 20% = 115 + 20% of 115 = 115 + $\frac{20\times 115}{100}=115+\frac{115}{5}=115+23=\mathit{R}\mathit{s}\mathbf{.}\mathbf{}\mathbf{138}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{(}\mathbf{}\mathit{A}\mathit{n}\mathit{s}\mathbf{}\mathbf{)}$