jainrahul1985 wrote:Tom is on a certain diet that requires him to limit the number of calories he takes in each day. He is allowed to take in 2400 calories each day from three square meals, and 200 calories each day from snacks and dessert combined. On some days, he splurges by taking in three times the recommended number of calories from snacks and dessert. The rest of the days, he deprives himself of snacks and dessert altogether. If his average calorie intake for a 10 day period was 2820, on how many days did he not splurge?
a)1 b)2 c)3 d)4 e)5
OA C
This is a weighted average/mixture question.
Deprived days = 2400.
Splurge days = 2400 + 3*200 = 3000.
Mixture = 2820.
The deprived days are being combined with the splurge days to yield a mixture with an average of 2820.
We can use alligation:
The proportion needed of each ingredient in the mixture is equal to the distance between the OTHER 2 averages.
Proportion of deprived days = |3000-2820| = 180.
Proportion of splurge days = |2400-2820| = 420.
Ratio of deprived days to splurge days = 180:420 = 3:7.
Thus, there were 3 deprived days and 7 splurge days.
The correct answer is
C.
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