a person solds an article for rupees 75 which costs him rupees x. he finds that he realised X% profit on his outlay. what is X equal to.
Answers
Answer:
x = Rs.50
Step-by-step explanation:
We have,
An article that costs Rs.x, and was then sold for Rs.75.
Also, is Gain percentage was x %.
Now,
C.P = Rs.x
S.P = Rs.75
Profit = S.P - C.P
P = 75 - x
Now,
Profit % = (Profit/C.P) × 100
But given,
P % = x %
So,
x = [(75 - x)/x] × 100
x/100 = (75 - x)/x
Cross multiplying we get,
x² = 100(75 - x)
x² = 7500 - 100x
x² + 100x - 7500 = 0
ax² + bx + c = 0
where a = 1, b = 100, c = -7500
Using Splitting the middle term method,
Sum = b = 100
Product = a × c = -7500
So, The factors are 150 and (-50).
Thus,
x² + 100x - 7500 = 0
x² + 150x - 50x - 7500 = 0
x(x + 150) - 50(x + 150)
(x + 150)(x - 50) = 0
So,
x = (-150) or x = 50
We know that, money can't have a negative value, unless for debts, since, here we are not dealing with debts,
x = Rs.50
We can also check this,
50 % = [(75 - 50)/50] × 100
50 % = (25/50) × 100
50 % = 50 %
Hence, it is correct.
Thus,
x = Rs.50
Hope it helped and believing you understood it........All the best