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CAT 1995 | Question: 180

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

PRODUCT M1 M2
P 10 8
Q 6 6

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

  1. 6 hours 30 minutes 
  2. 7 hours 24 minutes 
  3. 5 hours 48 minutes 
  4. 4 hours 6 minutes

1 Answer

1 1 vote

As the answer requires least number of machine hours required to produce 30 pieces of P and 25 pieces of Q

So, we'll go by which m/c takes less time to produce product p & product Q

M/C M2 consumes less time to produce product P

M/C M1 & M2 both consumes same time to produce product Q

Time taken by M2 to produce 30 pieces of P = 30 * 8 = 240 min

Time taken by M1 or M2 to produce 25 pieces of Q = 25 * 6 = 150 min

∴ Least number of machine hours required to produce 30 pieces of P and 25 pieces of Q  is (240 + 150)min = 390 min = 6hrs and 30min

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