Question

By selling an article what is the profit percent gained?
I. $5\% $ discount is given on list price
II. If discount is not given, $20\% $ profit is gained
III. The cost price of the articles is Rs. $5000$
A) Only I and II
B) Only II and III
C) Only I and III
D) All I, II and III
E) None of these

Answer 1

Hint: Discount on list price gives us the selling price which is a hundred minus discount percentage. Also, when the selling price is greater than the cost price then it is profit or gain. Here we will assume the unknown list price be “x”.

Complete step by step solution:
Let us assume the list price be “X” Rs.
Therefore, Selling price $S.P. = 95\% {\text{ of Rs}}{\text{.x}}$
Here, “of” suggests multiplication operator
$S.P. = x \times \dfrac{{95}}{{100}}$
Simplify the above expression –
$S.P. = \dfrac{{19x}}{{20}}$ …. (A)
When selling price is Rs. “x”
Gain $ = 20\% $
Cost price, $C.P. = Rs.\left( {\dfrac{{100}}{{120}} \times x} \right)$
Common factors from the numerator and the denominator cancel each other.
Cost price, $C.P. = Rs.\left( {\dfrac{{5x}}{6}} \right)$ …. (B)
Place the values of equation (A) and (B) in the gain formula –
Gain is the difference between the selling price and the cost price.
Gain $ = \left( {\dfrac{{19x}}{{20}} - \dfrac{{5x}}{6}} \right)$
Simplify the above expression by finding the LCM (least common multiple)
Gain $ = \left( {\dfrac{{57x - 50x}}{{60}}} \right)$
Gain $ = \left( {\dfrac{{7x}}{{60}}} \right)$
Gain $\% = \left( {\dfrac{{7x}}{{60}} \times \dfrac{6}{{5x}} \times 100} \right)\% $
Common factors are removed from the numerator and the denominator.
Gain $\% = 14\% $
Therefore, only I and II give us the answer.
Hence, from the given multiple choices option (A) is the correct answer.

Note:
Always remember that the percentage is defined as the numerator upon the hundred. Also, when there is profit – the selling price is always greater than the cost price while in loss cost price is greater than the selling price.