Percentage word problem

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adity_13: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Wed Aug 08, 2012 9:01 am

by adity_13 » Sat Mar 29, 2014 5:11 pm

Fresh watermelons contain 90% water by weight whereas dry watermelons contains 20% water by weight. what is the weight of dry watermelon obtained from 20kgs of fresh watermelon?

a: 2.4KG b: 2KG c: 2.5KG d: 1.6 KG e: Cannot be determined

Please explain how to solve it with detail.

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Source: Beat The GMAT — Data Sufficiency | Sat Mar 29, 2014 5:11 pm

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by Brent@GMATPrepNow » Sat Mar 29, 2014 11:21 pm

adity_13 wrote:Fresh watermelons contain 90% water by weight whereas dry watermelons contains 20% water by weight. what is the weight of dry watermelon obtained from 20kgs of fresh watermelon?

a: 2.4KG b: 2KG c: 2.5KG d: 1.6 KG e: Cannot be determined

Fresh watermelons contain 90% water by weight
We have 20 kg of fresh watermelons.
So, the composition of these 20 kg is as follows:
18 kg of water (i.e., 90%)
2 kg of non-water

IMPORTANT: to turn this batch into dry watermelon, some water must be removed? How much water? We don't know yet.

Let's let x = the weight of the water that must be removed in order to create dry watermelon.

Once the required amount of water has been removed, the weight of WATER in the dry watermelon will equal 18 - x kg

Also, once the required amount of water has been removed, the TOTAL weight of the BATCH will equal 20 - x kg

IMPORTANT: dry watermelon is 20% water by weight. In other words, dry watermelon is 1/5 water by weight.

So, we can write: (18 - x)/(20 - x) = 1/5
To solve this equation for x, first cross multiply: 5(18 - x) = 1(20 - x)
Expand: 90 - 5x = 20 - x
Rearrange: 70 = 4x
Solve: x = 17.5

So, 17.5 kg of water must be removed from the 20kg of fresh watermelon in order to get dry watermelon. So, the resulting batch will weigh 2.5 kg

Answer: C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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by GMATGuruNY » Sun Mar 30, 2014 3:34 am

adity_13 wrote:Fresh watermelons contain 90% water by weight whereas dry watermelons contains 20% water by weight. what is the weight of dry watermelon obtained from 20kgs of fresh watermelon?

a: 2.4KG b: 2KG c: 2.5KG d: 1.6 KG e: Cannot be determined

Please explain how to solve it with detail.

Fresh watermelon is 90% water, 10% nonwater.
Thus, the amount of NONWATER in 20kg of fresh watermelon = 10% of 20 = 2kg.

Dry watermelon is 20% water, 80% nonwater.
The fresh watermelon and the dry watermelon must contain the same amount of nonwater.
Thus, 80% of the correct answer choice must be equal to 2kg of nonwater.

We can PLUG IN THE ANSWERS, which represent the weight of the dry watermelon.
Answer choice C: 2.5kg
80% of 2.5 = 2kg.
Success!

The correct answer is C.

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