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Common Information

A health­drink company’s R&D department is trying to make various diet formulations, which can be used for certain specific purposes. It is considering a choice of 5 alternative ingredients (O, P, Q, R, and S), which can be used in different proportions in the formulations.

The table below gives the composition of these ingredients. The cost per unit of each of these ingredients is O: 150, P: 50, Q: 200, R: 500, S: 100.

Table below can be scrolled horizontally

Ingredient

Composition

Carbohydrate%

Protein%

Fat%

Minerals%

O

50

30

10

10

P

80

20

0

0

Q

10

30

50

10

R

5

50

40

5

S

45

50

0

5

Q.

Common Information Question: 3/4

Which among the following is the formulation having the lowest cost per unit for a diet having 10% fat and at least 30% protein? The diet has to be formed by mixing two ingredients.

 A.

P and Q

 B.

P and S

 C.

P and R

 D.

Q and S

 E.

R and S

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Solution:
Option(D) is correct

Consider the options.
Option (A):

P and Q have to be mixed in the proportion 4:1 to achieve 10% fat content. But this does not give 30% protein.

Option (B):

P and S do not contain fat.

Option (C):

P and R should be mixed in the proportion 3:1 to achieve 10% fat content. But 30% protein content is not achieved.

Option (D):

Q and S should be mixed in the proportion 1:4 to achieve 10% fat content and 46% protein content. The cost of this mix per unit would be 6/5.

Option (E):

R and S should be mixed in the proportion 1:3 to achieve 10% fat content and 50% protein content. The cost per unit of this mix would be 2.

Therefore, lowest cost is for Q and S.

Hence, option D.


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