Question

A tradesman marked his goods 30% above the CP. If he allows the discount of $6\dfrac{1}{4}\% $, then his gain percent is……
A. $24\dfrac{7}{8}\% $
B. 22%
C. $23\dfrac{3}{4}\% $
D. None of these

Answer 1

Hint: In order to solve this problem we need to assume the variable for CP and then apply the condition given in the question to get the right answer.

Complete step-by-step answer:
Let the cost price (CP) of the good be x.
As the tradesman marked his goods 30% above the C.P. we can say that the marked rate is:
\[ \Rightarrow {\text{x + }}\dfrac{{{\text{30x}}}}{{{\text{100}}}}{\text{ = 1}}{\text{.3x}}\]
It is given that he applies discount of $6\dfrac{1}{4}\% = \dfrac{{25}}{4}\% $ then we can say that he sells the good at:
$ \Rightarrow {\text{1}}{\text{.3x - }}\dfrac{{{\text{25x}}}}{{{{4 \times 100}}}} = {\text{1}}{\text{.3x - 0}}{\text{.0625x = 1}}{\text{.2375x}}$(Selling price)
Hence the difference between CP and SP is profit.
So,
SP – CP = Profit
1.2375x-x=0.2375x
Hence he got 0.2375x more money.
So, the percent he gains can be 0.2375 X 100 =23.75%
Hence the percent increase is 23.75%.
And 23.75% can be written as $23\dfrac{3}{4}\% $.
So, the correct option is C.

Note: To solve this problem we need to convert the given percentage into simple fraction from mixed fraction then we got the actual selling price after discount we found the SP is more than CP therefore we have done SP – CP to get profit. After getting the difference we multiplied it by 100 to get the percentage increase. Doing this will solve your problem. You should know that $a\dfrac{b}{c}$ can be written as $\dfrac{{ac + b}}{c}$.