CAT 1995 | Question: 179

Question

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

If M1 works at half its normal efficiency, what is the maximum number of units produced, if at least one unit of each must be produced?

• A. 96 
• B. 89 
• C. 100
• D. 119

Answer 1

M1 works at half of its normal efficiency - time taken to manufacture P  by M1 will be 10*2 min = 20 min

& time taken to manufacture Q by M1 will be 6*2 min = 12 min

time taken to manufacture P  by M2 8 min

time taken to manufacture Q  by M2  6 min

As, at least one unit of each product must be produced - one unit of product P will be manufactured by M2 as it takes less time to produce it.

So, time taken to produce one unit of product by M2 is 8 min

In the remaining time ((8 * 60) - 8) = 472 min M2 will produce product Q as it takes less time than product P

So, In the remaining 472 mins, M2 will produce $\dfrac{472}{6}$ = 78.6 units ≅ 78 units of product Q 

Total units produced by M2 in 8 hrs = (1 + 78) = 79 units

Now, m/c M1 can produce maximum $\dfrac{{8}*{60}}{12}$ = 40 units .

So, The maximum number of units produced, if at least one unit of each must be produced will be (79 + 40) units = 119 units