CAT Exam Model Paper 4 with solutions for free online practice

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Directions for questions 25 to 27: Answer the questions on the basis of the information given below.
Four machines A, B, C and D can produce four items E, F, G and H. The efficiency (in units/hr) of the machines for each product (while working alone on that product) is given in the table below

	E	F	G	H
A	75	150	125	50
B	125	75	100	100
C	100	125	125	75
D	125	75	75	125

Question : 25 of 60

Marks: +1, -0

If 5000 units each of E, F, G and H are required then which machine will take the least time if used alone?

Validate

Solution:

Total time taken (in hrs.) to produce 5000 units each of E, F, G and H:
For Machine A :

= { 5000 }/ { 75 } + { 5000 } /{ 150 } + { 5000 }/ { 125 } + { 5000 }/ { 50 }

= 5000 ( { 1 }/ { 75 } + { 1 } /{ 150 } + { 1 }/ { 125 } + { 1 }/ { 50 } )

= 200 ( { 1 }/ { 3 } + { 1 }/ { 6 } + { 1 }/ { 5 } + { 1 }/ { 2 } ) = 240

For Machine B :

= 5000 ( { 1 }/ { 125 } + { 1 } /{ 75 } + { 1 }/ { 100 } + { 1 } /{ 100 } )

= 200 ( { 1 }/{ 5 } + { 1 }/ { 3 } + { 1 }/ { 4 } + { 1 }/ { 4 } ) = 206.67

For Machine C :

= 5000 ( { 1 } /{ 100 } + { 1 } /{ 125 } + { 1 } /{ 125 } + { 1 }/ { 75 } )

= 200 ( { 1 }/ { 4 } + { 1 }/ { 5 } + { 1 }/ { 5 } + { 1 } /{ 3 } ) = 196.67

(least)
For Machine D:

= 5000 ( { 1 }/ { 125 } + { 1 } /{ 75 } + { 1 }/ { 75 } + { 1 }/ { 125 } )

= 200 ( { 1 }/ { 5 } + { 1 } /{ 3 } + { 1 }/ { 3 } + { 1 } /{ 5 } ) = 213.33

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