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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: 1/4

The company is planning to launch a balanced diet required for growth needs of adolescent children. This diet must contain at least 30% each of carbohydrate and protein, no more than 25% fat and at least 5% minerals.

Which one of the following combinations of equally mixed ingredients is feasible?

 A.

O and P

 B.

R and S

 C.

P and S

 D.

Q and R

 E.

O and S

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Solution:
Option(E) is correct

Table below can be scrolled horizontally

 

Carbohydrate

Protein

Fat

Minerals

O&P

65

25

5

5

R&S

25

50

20

5

P&S

62.5

35

0

2.5

Q&R

7.5

40

45

7.5

O&S

47.5

40

5

7.5

A mixture of O and S in equal proportion satisfies the given constraints as can be seen from the table above.
Hence, option E.

Alternatively,

As we want at least 30% carbohydrate and protein no more than 25% fat and at least 5% minerals.

∴ Take 10 gm of each in equal quantities.

Option (A) O = P = 10 gm.

Protein will only be 5 gm.

∴ 25% , (not satisfying the condition.)

Option (B) Carbohydrates is only 5 gm.

∴ Only 25% , (not satisfying the condition.)

Option (C) Minerals will be 0.5 gm.

∴ Only 2.5% (not satisfying the condition.)

Option (D) Carbohydrates will be 5.5 gm.

∴ 27.5% (not satisfying the condition.)

To verify option (E),

O = S = 10 gm.

Carbohydrate = 9.5 gm.

∴ 47.5%

Protein = 8 gm.

∴ 40%

Fat = 1 gm.

∴ 5%

Minerals = 1.5 gm.

∴ 7.5%

So, O and S will form the mixture.

Hence, option E.


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