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Machine Production Efficiency

CAT 1995 Slot 1 · Data Interpretation & Logical Reasoning · Medium · Data Interpretation

This is a medium Data Interpretation & Logical Reasoning question set from the CAT 1995 Slot 1 paper. It tests Data Interpretation. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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Passage / data set

Machine M1 as well as machine M2 can independently produce either product P or product Q. The time taken by machines M1 and M2 (in minutes) to produce one unit of product P and product Q are given in the table below (Each machine works 8 hours per day):

ProductM1 (min)M2 (min)
P108
Q66

Question 1 of 2

What is the maximum number of units that can be manufactured in one day?

  1. A.

    140

  2. B.

    160

  3. C.

    120

  4. D.

    180

Answer

B

Explanation

To maximize total units, manufacture product Q on both machines as Q takes minimum time (6 min per unit on both M1 and M2). Each machine works 8×60=4808 \times 60 = 480 minutes. Units by M1 =480/6=80= 480 / 6 = 80. Units by M2 =480/6=80= 480 / 6 = 80. Total maximum units =80+80=160= 80 + 80 = 160.

Question 2 of 2

What is the least number of machine hours required to produce 30 pieces of P and 25 pieces of Q respectively?

  1. A.

    6 hr 30 min

  2. B.

    7 hr 24 min

  3. C.

    6 hr 48 min

  4. D.

    4 hr 6 min

Answer

A

Explanation

To minimize time, produce P on M2 (takes 8 min vs 10 min) and Q on M1 (takes 6 min vs 6 min). Time for 30 P on M2 =30×8=240= 30 \times 8 = 240 min =4= 4 hours. Time for 25 Q on M1 =25×6=150= 25 \times 6 = 150 min =2.5= 2.5 hours =2= 2 hr 30 min. Total time =4+2.5=6.5= 4 + 2.5 = 6.5 hours =6= 6 hr 30 min.

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