Carol bought a toolbox for $X and then sold it for $Y, thereby earning a profit of 20%. Had the value of X been 15% less and the value of Y $76 less, Carol would have earned a profit of 30% . What was the value of X?
A. $400
B. $600
C. $640
D. $800
E. $840
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
Carol bought a toolbox for $X and then sold it for $Y
This topic has expert replies
GMAT/MBA Expert
-
Jay@ManhattanReview
- GMAT Instructor
- Posts: 3008
- Joined: Mon Aug 22, 2016 6:19 am
- Location: Grand Central / New York
- Thanked: 470 times
- Followed by:34 members
Then,
y = x + 20% of x = 1.2x;
Now,
New cost price = x – 15% of x = $0.85x;
New sale price = $(y – 76);
Revised profit = [{(y – 76) – 0.85x} / 0.85x]*100% = 30%
Replacing the value of y, we get
[{(1.2x – 76) – 0.85x} / 0.85x]*100% = 30%
Upon solving, we get x = $800
Correct answer: D
Hope this helps!
-Jay
_________________
Manhattan Review GMAT Prep
Locations: GMAT Prep Denver | SAT Prep Miami | GMAT Prep Europe | TOEFL Prep Los Angeles | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
ALTERNATIVE METHOD:
Let the cost price (CP) X be $100. Since the article was sold at a profit of 20%, its selling price (SP) would be $120.
We are given that If the toolbox had cost 15% less, its CP would have been $85. If the SP of the toolbox had been $76 less, then the profit would have been 30% of $85 = $25.5, or, that the SP would have been $85 + $25.5 = $110.5.
This means that a difference of (120 - 110.5)% = 9.5% corresponds to $76. Therefore, a difference of 100% would correspond to $800.
Answer: D
Let the cost price (CP) X be $100. Since the article was sold at a profit of 20%, its selling price (SP) would be $120.
We are given that If the toolbox had cost 15% less, its CP would have been $85. If the SP of the toolbox had been $76 less, then the profit would have been 30% of $85 = $25.5, or, that the SP would have been $85 + $25.5 = $110.5.
This means that a difference of (120 - 110.5)% = 9.5% corresponds to $76. Therefore, a difference of 100% would correspond to $800.
Answer: D
