Question

A man sells 35 waffles for Rs 15 each and loses Rs 40.4. If he sells 35 waffles for Rs 18, how much does he lose or gain?

Answer 1

Hint: First find the cost price of 35 waffles using the formula of loss which is equal to the subtraction of selling price from cost price. Selling price for 35 waffles is calculated by multiplying 35 by 15 and then substituting the value of selling price and loss of 40.4 in the loss formula we will get the cost price. Now, find the selling price for 35 waffles for Rs 18 by multiplying 35 by 18 and then compare this selling price with the cost price of 35 waffles and see whether the selling price is more or the cost price then accordingly find the loss or gain.

Complete step-by-step answer:
Selling price for 35 waffles at the rate of Rs 15 each is calculated by multiplying 35 by 15.
Selling price for 35 waffles at the rate of Rs 15 each is equal to:
 $ \begin{align}
  & 35\left( 15 \right) \\
 & =Rs525 \\
\end{align} $
Now, it is given that at this selling price the man has incurred a loss of Rs 40.4.
We know that loss is equal to:
 $ \text{Loss}=\left( C.P. \right)-\left( S.P. \right) $
Substituting the value of selling price as Rs 525 and loss as Rs 40.4 in the above equation we get,
 $ \begin{align}
  & 40.4=\left( C.P. \right)-\left( 525 \right) \\
 & \Rightarrow 40.4+525=C.P. \\
 & \Rightarrow C.P.=Rs565.4 \\
\end{align} $
We have got the cost price for 35 waffles which is equal to Rs 565.4.
Now, the man has sold 35 waffles at the rate of Rs 18 each so new selling price for 35 waffles is calculated at this new rate by multiplying 35 by 18 we get,
New selling price is equal to:
 $ \begin{align}
  & Rs\left( 35\times 18 \right) \\
 & =Rs630 \\
\end{align} $
We have to find out whether at this selling price the man has incurred loss or gain.
In the above solution, we have calculated the cost price for 35 waffles as Rs 565.4. Now, comparing this cost price with the new selling price you can see that the selling price is more than the cost price. This implies that the man has undergone profit and the subtraction of cost price from the selling price will give us the value of profit.
 $ \begin{align}
  & \text{Profit}=\left( S.P. \right)-\left( C.P. \right) \\
 & \Rightarrow \text{Profit}=Rs\left( 630-565.4 \right) \\
 & \Rightarrow \text{Profit}=Rs\left( 64.6 \right) \\
\end{align} $
Hence, the man has incurred a profit of Rs 64.6 on the selling price of 35 waffles at the rate of Rs 18 each.

Note: You might have confused remembering the formula for profit and loss like when the selling price will come first and when the cost price will come first.
In the below, we are writing the formula for profit and loss.
 $ \text{Loss}=\left( C.P. \right)-\left( S.P. \right) $
 $ \text{Profit}=\left( S.P. \right)-\left( C.P. \right) $
Now, the trick to remember the formula is that whenever loss occurs then cost price is greater than selling price and whenever profit occurs then selling price is greater than cost price.