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CAT 2007 — DILR Question 21

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Passage / Data

Answer the following question based on the information given below.

A health-drink 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.

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In what proportion should P, Q and S be mixed to make a diet having at least 60% carbohydrate at the lowest per unit cost?

Answer & solution

Correct answer: 4 : 1 : 1

  • A

    2 : 1 : 3

  • B

    4 : 1 : 2

  • C

    2 : 1 : 4

  • D

    3 : 1: 2

  • 4 : 1 : 1

Solution

P, Q and S contain 80%, 10% and 45% carbohydrates.

To achieve 60% carbohydrates, proportion of P should be maximum. Hence, options 1 and 3 are eliminated.

Option 2: Carbohydrate content = (320 + 10 + 90)/700 = 420/700 = 60%

Cost per unit = (200 + 200 + 200)/700 = 6/7 = 0.857

Option 4: Carbohydrate content = (240 + 10 + 90)/600 < 60%

Option 5: Carbohydrate content = (320 + 10 + 45)/600 = 62.5%

Cost per unit = (200 + 200 + 100)/600 = 5/6 = 0. 833

P, Q and S in the proportion 4 : 1 : 1 has the lowest cost per unit.

Hence, option (e).

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CAT 2007 DILR Q21: In what proportion should P, Q and S be mixed to make a diet having at least 60% carbohydrate at the lowest pe — Solution | TheCATExam