Question

A seller sells his product on $14\%$ profit of the market price. If the selling price is 3420 then the market price is equal to:
(a) 3000
(b) 3100
(c) 2800
(d) 2846

Answer 1

Hint: Let us assume that the market price as Rs x then the seller sells his product at the profit of $14\%$ so find the selling price (S.P.) of x at the profit of $14\%$ which we are going to find by the following formula $S.P.=x+x\left( \dfrac{\text{Profit}}{100} \right)$. Then it is given that the selling price of the product is equal to 3420 so equating this formula of selling price to 3420. Solving this equation will give you the value of x.

Complete step-by-step answer:
We have given the profit percentage at which a seller sells his product which is $14\%$ and the selling price of the product is 3420 and we have to find the market price of the product.
Let us assume that the market price of the product is Rs x.
We know that profit on any price say y Rs at the rate of $z\%$ is calculated by adding the original price that is y to the $z\%$ of y which we are shown below:
$\text{Profit}=y+y\left( \dfrac{z}{100} \right)$
And then the selling price (S.P.) of the product at a profit of $14\%$ on x is actually a profit on the market price at the rate of $14\%$ is equal to:
$S.P.=x+x\left( \dfrac{14}{100} \right)$
Taking x as common in the above equation we get,
$\begin{align}
  & S.P.=x\left( 1+\dfrac{14}{100} \right) \\
 & \Rightarrow S.P.=x\left( \dfrac{100+14}{100} \right) \\
 & \Rightarrow S.P.=x\left( \dfrac{114}{100} \right) \\
\end{align}$
It is given that selling price of the product is Rs 3420 so equating the above selling price to 3420 we get,
$x\left( \dfrac{114}{100} \right)=3420$
Dividing 114 on both the sides we get,
$\begin{align}
  & x\left( \dfrac{1}{100} \right)=\dfrac{3420}{114} \\
 & \Rightarrow \left( \dfrac{x}{100} \right)=30 \\
\end{align}$
Multiplying 100 on both the sides we get,
$\begin{align}
  & x=30\left( 100 \right) \\
 & \Rightarrow x=3000 \\
\end{align}$
Hence, we have got the market price as Rs 3000.
Hence, the correct option is (a).

Note: You can check whether the market price that we are getting is correct or not by taking $14\%$ of 3000 and then adding it to 3000 to see what selling price we are getting.
$\begin{align}
  & 3000+3000\left( \dfrac{14}{100} \right) \\
 & \\
\end{align}$
Taking 3000 as common in the above equation we get,
$3000\left( 1+\dfrac{14}{100} \right)$
$\begin{align}
  & =3000\left( \dfrac{100+14}{100} \right) \\
 & =3000\left( \dfrac{114}{100} \right) \\
\end{align}$
Two zeros in the numerator and denominator will be cancelled out and we are left with:
$\begin{align}
  & 30\left( 114 \right) \\
 & =3420 \\
\end{align}$
As you can see that the selling price we have got is the same as given in the above question so the market price that we have solved above is correct.