Time and Work
Aptitude

 Back to Questions
Q.

In Nuts And Bolts factory, one machine produces only nuts at the rate of 100 nuts per minute and needs to be cleaned for 5 minutes after production of every 1000 nuts.

Another machine produces only bolts at the rate of 75 bolts per minute and needs to cleaned for10 minutes after production of every 1500 bolts.

If both the machines start production at the same time, what is the minimum duration required for producing 9000 pairs of nuts and bolts?

 A.

130 minutes

 B.

135 minutes

 C.

170 minutes

 D.

180 minutes

 Hide Ans

Solution:
Option(C) is correct

Machine I:

Number of nuts produced in one minute = 100

To produce 1000 nuts time required = 10 min

Cleaning time for nuts = 5 min

Over all time to produce 1000 nuts = 15 min.

Over all time to produce 9000 = 135 min − 5 min = 130 min -----(1)

Machine II:

To produce 75 bolts time required = 1min

To produce 1500 bolts time required = 20 min

Cleaning time for bolts = 10 min.

Effective time to produce 1500 bolts = 30 min

Effective time to produce 9000 bolts = 30×6 − 10 = 170 min ------ (2)

From (1) and (2),

Minimum time = 170 minutes

Edit: Thank you Najaf for pointing out the typo in the solution, modified solution and in part A, time has been changed to 130 min from 133 min.


(4) Comment(s)


Additi
 ()

Minimum time should be 130 because part A is producing 9000 pairs in 130 min whereas part B is producing 9000 pairs in 170 minute, if i am wrong correct me ?



Shubh
 ()

why 5 cycles and not 6?



Najaf
 ()

To produce 9,000 nuts:

(Production Time of 1,000 nuts x 9) + Cleaning Time for 8 cycles

$ \Rightarrow (9 \times 10 \text{ mins}) + (5 \times 8 \text{ mins}) = 130\text{ mins}$

To produce 9,000 bolts:

(Production Time of 1,500 bolts x 6) + Cleaning Time for 5 cycles

$ \Rightarrow (6 \times 20 \text{ mins}) + (5 \times 10 \text{ mins}) = 170  \text{ mins}$

So according to my calculation, part A (nut production) is done wrong.


Deepak
 ()

Thank you, modified the solution accordingly.