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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: 2/4

For a recuperating patient, the doctor recommended a diet containing 10% minerals and at least 30% protein. In how many different ways can we prepare this diet by mixing at least two ingredients?

 A.

One

 B.

Two

 C.

Three

 D.

Four

 E.

None

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Solution:
Option(A) is correct

The diet should contain 10% minerals.

P contains no minerals.

∴ P cannot be a part of any mixture.

R and S both contain 5% minerals.

∴ Mix of R and S in any proportion cannot give 10% minerals.

Consider O and R in the proportion x:y

∴ 10x + 5y = 10(x + y)

∴ 5y = 10y, which is not possible.

Similarly, Q and S, O and S, and Q and R are not possible.

Similarly a mix of three ingredients is not possible.

∴ The only possible mix is that of O and Q in equal proportion.

Hence, option A.


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