Question

The selling price of 18 oranges is equal to the cost price of 16 oranges. Find loss percent.
Mark 1 if the answer is \[11\dfrac{1}{9}\%\] otherwise mark 0.

Answer 1

Hint: We will assume $x$ as the selling price of 18 oranges and also cost price of 16 oranges.
Then, we will find the SP and CP of one orange. And use the formula that loss is equal to selling price
subtracted from cost price, i.e. loss= C.P-S.P. Loss percentage is the amount of loss with respect to
cost price followed by multiplication by 100 which are shown in the following by the formula as follows: $loss\%=\dfrac{loss}{C.P.}\times 100$.

Complete step by step answer:
From the problem the given information is,
Let the cost price of 1 orange = $x$
Then cost price of 16 oranges = $16x$
From the problem it is given that the selling price of 18 oranges is equal to the cost price of 16 oranges.
That can be written as follows,
S.P of 18 oranges = $16x$
Therefore, the selling price of 1 orange is equal to:
$\dfrac{16x}{18}$
Dividing numerator and denominator by 2 we get,
$\dfrac{8x}{9}$
 As cost price is more than selling price here we will get the loss.
Loss = Cost price – Selling Price
Loss = $18x-16x$
On simplifying, we loss as follows
Loss = $2x$
Now we have calculate the percentage of loss as follows
$\%Loss=\dfrac{Loss}{\operatorname{C}.P}\times 100$(Here C.P is cost price)
On substituting values of Loss and Cost price in the above equation we get as follows
$\%Loss=\dfrac{2x}{18x}\times 100$
On simplifying we get as follows
$\%Loss=\dfrac{100}{9}=11.1$
We can write the above loss percentage in terms of mixed fraction as follows:
$\%Loss=11\dfrac{1}{9}$

Therefore, according to the question we can mark it as 1.

Note: The mistake that could happen in this problem is that in the formula of loss instead of subtracting selling price from cost price you might have subtracted cost price from selling price.
The correct formula of loss is equal to:
$C.P.-S.P.$
The incorrect formula of loss which you might write is as follows:
$S.P.-C.P.$
The trick to get the expression of loss as right is as follows: if you mistakenly subtract cost price from selling price then you will get negative value of loss then you will know that you have wrongly subtracted cost price and selling price so interchange the positions of cost price and selling price so that you can get the positive value of loss.