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Percentage Increase

by [email protected] » Tue Apr 22, 2014 3:41 am
The farmer spent 40% money (i.e. 35 $) on the chicken feed (which he bough at a 20% discount) now if we have to take out the original amount can we do it this way?

40% of 35 dollar is 14 and 120% of 14 is 16.8- Is this the right way to derive the original cost of the chicken feed or im doing some technical mistake here?

Please explain-Thanks
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by GMATGuruNY » Tue Apr 22, 2014 6:24 am
A farmer spent $35 on feed for chickens and goats. He spent 40% money on chicken feed, which he bought at a 20% discount off the full price, and spent the rest on goat feed, which he bought at full price. If the farmer had paid full price for both the chicken feed and the goat feed, what amount would he have spent on the chicken feed and goat feed combined?

A. $37.80
B. $38.50
C. $39.20
D. $39.50
E. $40.60
We need to determine the following ratio:
(full price)/(actual amount spent).

To determine this ratio, plug in an EASY VALUE for the full price of chicken feed.
Since the chicken feed is discounted by 20% -- the equivalent of 1/5 -- let the regular price of chicken feed = $5.

Then:
After the 1/5 discount, the amount spent on chicken feed = 5 - (1/5)*5 = 4.
Since the amount spent on chicken feed represents 40% -- the equivalent of 4/10 -- of the total amount spent, the total amount spent = $10, while the amount spent on goat feed = $6.
Resulting values:
Full price = (regular chicken feed price) + (regular goat feed price) = 5+6 = 11.
Actual amount spent = (regular chicken feed price) + (regular goat feed price) = 4+6 = 10.
Thus:
(full price)/(actual amount spent) = 11/10.

The resulting ratio implies that the full price is equal to 11/10 of the actual amount spent ($35):
(11/10) * 35 = (11/2) * 7 = 77/2 = 38.5.

The correct answer is B.
Last edited by GMATGuruNY on Tue Apr 22, 2014 7:15 am, edited 1 time in total.
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by Brent@GMATPrepNow » Tue Apr 22, 2014 6:24 am
A farmer spent $35 on feed for chickens and goats. He spent 40% of the money on chicken feed, which he bought at a 20% discount off the full price, and spent the rest on goat feed, which he bought at full price. If the farmer had paid full price for both the chicken feed and the goat feed, what amount would he have spent on the chicken feed and goat feed combined?

A. $37.80
B. $38.50
C. $39.20
D. $39.50
E. $40.60
He spent 40% (of the $35) on chicken feed.
40% of $35 = $14. So, he spent $14 on chicken feed.

He got a 20% discount on the chicken feed.
In other words, he paid 80% of the original price.
So, let C = original price of chicken feed.
We can write 80% of C = $14
Or we can write 0.8C = $14
Or, even better, (4/5)C = $14

To solve for C, we'll multiply both sides by 5/4 to get: C = (14)(5/4) = 17 1/2
So, the original price of the chicken feed = $17.5

Finally, if the farmer spent $14 (of the original $35) on chicken feed, then he spent the remaining $21 on goat feed (at no discount).

So, without the discount, the farmer would have paid $17.5 + $21 =[spoiler] $38.50 = B[/spoiler]

Cheers,
Brent
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by Brent@GMATPrepNow » Tue Apr 22, 2014 6:30 am
[email protected] wrote:
40% of 35 dollar is 14 and 120% of 14 is 16.8- Is this the right way to derive the original cost of the chicken feed or im doing some technical mistake here?
This is a common error.
If the sale price is 20% less than the original price, we CANNOT conclude that the original price is 20% greater than the sale price.

Consider this example: If the original price is $5 and the sale price is $4, then the sale price is 20% less than the original price. HOWEVER, the original price ($5) is NOT 20% more than the sale price ($4). The original price is 25% more than the sale price .

Cheers,
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