Time and Work
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Q.

A factory produces nuts and bolts. A machine in it produces only nuts while another produces only bolts. The machine producing only nuts produces 400 nuts per minute and need to be cleared for 15 minutes after production of 2000 nuts. The machine producing only bolts produces 300 bolts per minute and needs to be cleared for 15 minutes after production of 3000 bolts. Find the minimum time required to produce 12000 pairs of bolts and nuts if both machines are operated simultaneously.

 A.

85 minutes

 B.

105 minutes

 C.

100 minutes

 D.

115 minutes

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Solution:
Option(B) is correct

The nut machine makes 400 nuts per min and 2000 nuts in 5 min.

Then it has to be cleared for 15 min

To produce 12,000 nuts, time required = $5(20)+15=105$ min

The bolt machine makes 300 bolts per min and 3000 bolts in 10 min

Then it has to be cleared for 15 min

To produce 12000 bolts, time required = $3(25)+10=85$ min

In both the cases, we may ignore the time needed for cleaning, after the last lots are produced.

We see that the time required is 105 min.


(4) Comment(s)


Hari Krishna
 ()

5(20)+15=115 not 105 .......u do miscalculation ... improve it.


Hari Krishna
 ()

ans is d not b ..............


Saif Pathan
 ()

400 nuts in 1 min

i.e 2000 nuts in 5 mins + 15min for clearing

which makes 2000 nuts for every 20 mins

and for 12000 nuts time reqd is $\dfrac{(12000*20)}{2000} = 120$

Similarly, for bolts, it takes 100 mins for 12000 nuts,

So, the time required to make 12000 pairs of nut and bolt is 120 mins.


Renu
 ()

In case of nut machine,

The last time you don't need to clean for 15 min. So it will be $120-15=105$ min only.