Carol bought a toolbox for $X and then sold it for $Y

[Mikrislac]

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

[Jay@ManhattanReview]

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

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
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[Mikrislac]

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