total on a day =2400 + 200 =2600
for 10 days total =26000
average =2720
so total as per this average for 10 days =27200
excess =1200
now in some days he took excess of 400 (600-200)
so this excess of 400 he must have consumed for 3 days to accommodate the excess of 1200
hence answer =3

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.

Ingredient 1: Caloric intake on deprived days = 2400.
Ingredient 2: Caloric intake on splurge days = 2400 + 3*200 = 3000.
Mixture: Caloric intake for the MIXTURE of days = 2820.

Let D = the number of deprived days and S = the number of splurge days.
To determine the ratio of D to S in the mixture, use ALLIGATION:

Step 1: Plot the 3 averages on a number line, with the averages for the two ingredients on the ends and the mixture average in the middle.
D 2400---------------2820--------------3000 S

Step 2: Calculate the distances between the averages.
D 2400-----420-----2820-----180-----3000 S

Step 3: Determine the ratio in the mixture.
The required ratio of D to S is the RECIPROCAL of the distances in red.
D:S = 180:420 = 3:7.

Thus, of the 10 days, D=3 and S=7.

The correct answer is C.

For two similar problems, check here:

https://www.beatthegmat.com/ratios-fract ... 15365.html

@GMATGuruNY : Hi why are we considering one of the end poles to be 2400 and not 2600 ?
2600---2820------3000 ( Why is this not the correct number line) ?

Deepthi Subbu wrote:@GMATGuruNY : Hi why are we considering one of the end poles to be 2400 and not 2600 ?
2600---2820------3000 ( Why is this not the correct number line) ?

From the problem:
The rest of the days, he deprives himself of snacks and dessert altogether..
Thus, on deprived days, Tom takes in only 2400 calories from three square meals.