Question

By Selling a product for Rs.$100$ how much profit was earned?
$\left( \text{i} \right)$ 20% profit would have been earned if it had been sold for Rs.$90$.
$\left( \text{ii} \right)$The profit was one-third of the cost price.
A. Statement $\left( \text{i} \right)$ alone is sufficient, but statement $\left( \text{ii} \right)$ alone is not sufficient.
B. Statement $\left( \text{ii} \right)$ alone is sufficient, but statement $\left( \text{i} \right)$ alone is not sufficient.
C. Both statements together are sufficient, but neither statement alone sufficient.
D. Each statement alone is sufficient.

Answer 1

Hint: For this problem we need to calculate the cost price to get the value of profit for both the statements. Now comparing the values obtained from the both the statements we will mark an option as the correct option.

Complete step by step answer:
$\left( \text{i} \right)$Given that, Selling Price of the Product is Rs.$100$
The percentage of profit is $20\%$(from statement $\left( \text{i} \right)$)
Let the Cost price is $x$, then Profit is
$\begin{align}
  & \text{Profit}=\text{S}\text{.P}-\text{C}\text{.P} \\
 & \text{=}100-x
\end{align}$
And the profit percentage is
$\begin{align}
  & \text{Profit }\!\!\%\!\!\text{ }=\dfrac{\text{Profit}}{\text{Cost Price}}\times 100 \\
 & =\dfrac{100-x}{x}\times 100
\end{align}$
In the problem they mentioned profit percentage as $20\%$, then
$\dfrac{100-x}{x}\times 100=20$
So, from the above equation we can find the cost price of the product.
$\therefore $ Profit can be calculated from the statement $\left( \text{i} \right)$ alone.

$\left( \text{ii} \right)$Given that, Cost Price is one-third of the profit then
$\text{C}\text{.P}\times \dfrac{1}{3}=\text{P}.....\left( \text{a} \right)$
But we know $\text{C}\text{.P}=x$ and
$\begin{align}
  & \text{P}=\text{S}\text{.P}-\text{C}\text{.P} \\
 & \text{=100}-x
\end{align}$
Then from equation $\left( \text{a} \right)$, we have
$x\times \dfrac{1}{3}=100-x$
From the above equation also, we can find the value of Profit.
So, Profit can be calculated from the statement $\left( \text{ii} \right)$ alone.

So, the correct answer is “Option D”.

Note: In this problem we have used the terms Profit, Selling Price, Cost rice and they are defined as below
Cost Price (CP): The cost price is the amount of money spent on making the product. For example, if Leela is making cotton skirts, the amount of money spent on getting the cotton fabric, buttons, and other materials are referred to as the cost price.
Selling Price (SP): After investing in making a product, a businessman always aims to earn more than what he spent. So, in this case, Leela is selling her skirts at a price above her cost price. The cost at which the product is sold is called Selling Price. It is the price the customer (buyer) pays for the product.
Profit (P): In math, profit is the difference between the selling price and the cost price. But only if the SP > CP, then there is a profit.
Profit percentage: We can write profit percentage as
Profit Percentage $=\dfrac{\text{Profit}}{\text{Cost Price}}\times 100$