The production cost of an item increased by 20% and the government also started taxing the item 10% on the selling price. The percentage increase in the selling price which will ensure profit remains the same would be ____

in Pre-Algebra Answers by (440 points)

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

Let the cost of the item be c, then the increased cost is 1.2c.

Let s₁ be the original selling price. Let the new selling price before tax be s₂ then after tax it will be 1.1s₂. The original profit is s₁-c. The new profit is 1.1s₂-1.2c=s₁-c, because the profit is to remain unchanged. Therefore 1.1s₂-s₁=0.2c. If we divide through by s₁ we get 1.1(s₂/s₁)=1+0.2c/s₁. So s₂/s₁=(1+0.2c/s₁)/1.1. If s₂=s₁+rs₁/100 where r is the percentage increase in selling price, then s₂/s₁=1+r/100=(1+0.2c/s₁)/1.1. r/100=(1+0.2c/s₁)/1.1-1=(0.2c/s₁-0.1)/1.1 and r=100(0.2c/s₁-0.1)/1.1=10(2c/s₁-1)/1.1.

This implies a negative value for r, which means a reduction in the selling price, since c/s₁ is 1/(original markup ratio).

by Top Rated User (599k points)

Related questions

1 answer
0 answers
asked Sep 6, 2012 in Word Problem Answers by anonymous | 588 views
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
81,951 questions
86,346 answers
2,238 comments
71,626 users