Cost of an article is first decreased by 25% and then further decreased by 40% find the percentage change in the cost of the article
Answers
Step-by-step explanation:
Given :-
Cost of an article is first decreased by 25% and then further decreased by 40%
To find :-
Find the percentage change in the cost of the article ?
Solution :-
Let the Cost Price of the article be Rs. X
Decreased percentage in the Cost Price = 25%
Decreasing in the Cost Price = 25% of Cost Price
=> 25% of X
=> 25% × X
=> (25/100)×X
=> (1/4)×X
=> X/4
The Cost Price of the article after decreasing
=> X-(X/4)
=> (4X-X)/4
=> 3X/4
and
Again it is decreased by 40%
Decreasing in the Cost Price = 40% of Cost Price
=> 40% of (3X/4)
=> 40% × (3X/4)
=> (40/100)×(3X/4)
=> (2/5)×(3X/4)
=> (2×3X)/(5×4)
=> 6X/20
=> 3X/10
The Cost Price of the article after decreasing
=> (3X/4)-(3X/10)
=> 3X[(1/4)-(1/10)]
LCM of 4 and 10 = 20
=> 3X[(5-2)/20]
=> 3X[(3/20)
=> 9X/20
The Cost Price of the article becomes Rs. 9X/20
The Original Cost Price = Rs. X
The new Cost Price = Rs. 9X/20
Original Cost Price > New Cost Price
There is decreasing occured
=> Decreasing in the Cost Price
=> Original Price - New Price
=> X-(9X/20)
=> (20X-9X)/20
=> 11X/20
Decreased % = (Decreased amount in the Cost Price/Original Price ) ×100
=> Decreased% = [(11X/20)/X]×100
=> Decreased% = (11X/20X)×100
=> Decreased% = (11/20)×100
=> Decreased% = 1100/20
=> Decreased% = 55%
Answer:-
The decreased percentage in the cost price of the article is 55%