Question

A dealer sells an article for Rs.75 and gains as much percent as the cost price of the article. what is the cost price of the article ?

Answer 1

⭐️⭐️⭐️⭐️⭐️❤️❤️❤️❤️❤️❤️❤️❤️


SP=75 Rs.
Let the profit% is x%.
So the cost price is x Rs.

Profit= SP- CP
= 75-x Rs.


Profit%= (profit/CP)×100
x= (75-x)/x ×100
x^2= (75-x)×100
x^2 = 7500-100x.
x^2+100x-7500=0.
x^2 + 150x-50x-7500=0.
x(x+150)-50(x+150)=0.
(x-50)(x+150)=0.

Root 1
x-50=0
x=50

Root 2
x+150=0
x=-150 coz the value of x cannot be 0 we'll discard this value.

Hence the cost price is 50Rs
And profit% is 50%.

❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️

Answer 2

Hey mate!

Given, selling price of article = Rs 75

Let the cost price of the article = Rs x.

We know that,

$profit \: percent \: = \frac{profit}{C.P} \times 100$
It is given that the profit percent is equal to the cost price of the price

∴ Profit percent = x

On putting values in (1), we get

$x = \frac{ S.P - C.P. }{ C.P } \times 100 \\ \\ x = \frac{75 - x}{x} \times 100 \\ \\ x {}^{2} = 7500 - 100x \\ \\ x {}^{2} + 100x - 7500 = 0 \\ \\ x {}^{2} + 150x - 50x - 7500 = 0 \\ \\ x(x + 150) - 50(x + 150) \\ \\ (x + 150)(x - 50)$

•°• x = -150 and x = 50

Since the C. P cannot be negative

∴ x  ≠ –150

Hence the cost price of article be Rs 50.

thank you!!