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CAT 1991 — QA Question 28

BasicsEasy
Passage / Data

Answer the following questions based on the information given below:

There were a hundred schools in a town. Of these, the number of schools having a play – ground was 30, and these schools had neither a library nor a laboratory. The number of schools having a laboratory alone was twice the number of those having a library only. The number of schools having a laboratory as  well as a library was one fourth the number of those having a laboratory alone. The number of schools  having either a laboratory or a library or both was 35.

Three machines, A, B and C can be used to produce a product. Machine A will take 60 hours to produce a million units. Machine B is twice as fast as Machine A. Machine C will take the same amount of time to produce a million units as A and B running together. How much time will be required to produce a million units if all the three machines are used simultaneously? (in hous)

Answer & solution

  • A

    12

  • 10

  • C

    8

  • D

    6

Solution

B being twice as fast as A, will take half of time of A to produce a million units i.e. = 30 hrs.

Since, Machine C takes the same amount of time as A & B running together,

∴ 1C = 1A + 1B or

1A + 1B + 1C = 2A + 2B

⇒ 1A + 1B + 1C = 2(1A+1B) = 2(160+130) = 110

Hence, it will take 10 hours for all three of them to produce 1 million units.

Hence, option (b).

CAT 1991 QA Q28: Three machines, A, B and C can be used to produce a product. Machine A will take 60 hours to produce a million — Solution | TheCATExam