Question

When a commodity is solid for Rs. $34.80,$there is a loss of $2\% $. What is the cost price of the commodity?
A. $Rs.{\text{ 26}}{\text{.10}}$
B. $Rs.{\text{ 43}}$
C. $Rs.{\text{ 43}}{\text{.20}}$
D. $Rs.{\text{ 46}}{\text{.40}}$

Answer 1

Hint: First of all we will suppose the unknown term cost price of the commodity equal to “x” and then will find the correlation between the known terms and the unknown terms and will simplify for the required value.

Complete step by step answer:
Let us suppose the cost price of the commodity be equal to Rs. “x”
Given that loss $ = 25\% $
Therefore, loss $ = 25\% = 0.25x$
Also, given that the selling price of the commodity $ = Rs.{\text{ 34}}{\text{.80}}$
Now, loss can be given by the difference between the selling price and the cost price.
Cost Price $ - $loss $ = $selling price
$x - 0.25x = 34.80$
Simplify the above equation-
$0.75x = 34.80$
Term multiplicative on one side if moved to the opposite side then it goes to the denominator.
$x = \dfrac{{34.80}}{{0.75}}$
Re-write the above equation removing the decimal point. Always count the number of digits after the decimal point and then put zeros under it or ten for one digit, hundred for two digits and so on.
$x = \dfrac{{\dfrac{{3480}}{{100}}}}{{\dfrac{{75}}{{100}}}}$
Simplify
$x = \dfrac{{3480 \times 100}}{{75 \times 100}}$
Common terms from the numerator and the denominator cancels each other.
$x = \dfrac{{3480}}{{75}}$
Simplify finding the division of the term on the denominator with the numerator.
$x = 46.4$Rs.

Hence, from the given multiple choices – the option D is the correct answer.

Note: Be good in multiples and always remember that common factor from the numerator and the denominator cancel each other. Also be careful while removing the decimal point. Always count the number of digits after the decimal point and then put zeros under it or ten for one digit, hundred for two digits and so on. Be good in finding the factors of the numbers and then remove common factors from the numerator and the denominator.