A trader bought a number of articles for Rs. 900, five were damaged and he sold each of the rest at Rs. 2 more than what he paid for it, thus getting a profit of Rs. 80 on the whole transaction. Find the number of articles he bought.
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Answers
Solution:-
Let the Number of Articles be "x" and cost of each particle be ₹y.
=) Cost of "x" Number of Article = xy
=) 900 = xy
=) y = 900/x [ Cost of 1 Article ]
A.T.Q.
Given that five were damaged and he sold each of the rest at Rs. 2 more than what he paid for it, thus getting a profit of ₹80.
=) ( x -5)( y + 2)= 900 + 80
=) xy - 2x - 5y + - 10 = 980
=) x (900/x) - 2x - 5 ( 900/x) -10 - 980 = 0
=) 900 - 2x - 4500/x - 990 = 0
=) 2x - 4500/x - 90 = 0
=) [ 2x² - 4500 - 90x ]/x = 0
=) 2x² - 90x - 4500 = 0
=) 2 [ x² - 45x - 2250] = 0
=) x² - 45x - 2250 = 0
=) x² - ( 75 - 30 )x - 2250 = 0
=) x² - 75x + 30x - 2250 = 0
=) x ( x - 75 ) + 30 ( x - 75) = 0
=) [ x = 75 ] and [ x = -30 ] ( Neglect)
Hence,
Number of Articles = x = 75.
Answer : 75 articles
Step by step explanation :
To find : Total number of articles
Solution :
Let us assume the number of articles as 'x'
Given that,
He paid a total of Rs. 900
Cost price of an article = 900/x Rs.
Next, 5 articles were damaged ones.
So, we can say that,
(x - 5) articles are undamaged.
Selling price : (900/x) + 2
= ( 900 + 2x )/ x
Now, As given,
Profit = Rs 80
Total selling price : 900 + 80 = 980 Rs.
.°. ( x - 5 ) × ( [900 + 2x ] / x ) = 980
» ( x - 5 ) × [ 900 + 2x ] = 980 × x
» 2x² + 890x - 4500 = 980x
» 2x² + 90x - 4500 = 0
Dividing both sides by 2,
» x² - 45x - 2250 = 0
Splitting the middle term,
» x² - 75x + 30x - 2250 = 0
» x(x - 75) + 30( x - 75 ) = 0
» ( x + 30 ) ( x - 75 ) = 0
» x = - 30 or x = 75
Here,
x = -30 can't be accepted.
.°. x = Number of articles = 75
Answer : Total number of articles are 75.