Question: A rabbit on a controlled diet is fed daily 300 grams of a mixture of two foods, food X and food Y. food X contains 10% protein and food Y contains 15% protein. If the rabbit’s diet provides exactly 38 grams of protein daily, how many grams of food X are in the mixture?

1. 100
2. 140
3. 150
4. 160
5. 200

“A rabbit on a controlled diet is fed daily 300 grams of a mixture of two foods, food X and food Y. food X contains 10% protein and food Y contains 15% protein. If the rabbit’s diet provides exactly 38 grams of protein daily, how many grams of food X are in the mixture?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Answer:

Approach Solution (1):

38 grams means approx 12.66%. Then use the mixture allegation formula to calculate the ratio of X to Y i.e.,

\(\frac{X}{Y}=\frac{15-12.66}{12.66-10}=\frac{2.33}{2.66}\)

Hence amount of X in the total mixture is \(\frac{300*2.33}{2.33+2.66}=139.6\approx140\)

Correct option: B

Approach Solution (2):

We know that
1.00 x + 1.00 y = 300

And that
0.10 x + 0.15 y = 38

So

0.10 x + 0.15 y = 38 * 10 = 1.00 x + 1.50 y = 380
Align them under each other

1.00 x + 1.50 y = 380
1.00 x + 1.00 y = 300

Means 0.50 y = 80

80 * 2 = 160
y = 160
x = 300 – y
x = 300 – 160
x = 140

Correct option: B

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