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### Discussion :: Time and Work

1. How long will Machine Y, working alone, take to produce x candles?

I. Machine X produces x candles in 5 minutes.

II. Machine X and Machine Y working at the same time produce x candles in 2 minutes.

2.  A. I alone sufficient while II alone not sufficient to answer B. II alone sufficient while I alone not sufficient to answer C. Either I or II alone sufficient to answer D. Both I and II are not sufficient to answer E. Both I and II are necessary to answer

Answer : Option E

Explanation :

I. gives, Machine X produces$$\frac { X } { 2 }$$candles in 1 min

II. gives, Machine X and Y produce$$\frac { X } { 2 }$$candles in 1 min

From I and II, Y produces[$$\frac { X } { 2 }$$-$$\frac { X } { 5}$$]=$$\frac {3 X } { 10 }$$candles in 1 min

$$\frac {3 X } { 10 }$$candles are produced by Y in 1 min

x candles will be produced by Y in[$$\frac { 1 0} { 3X }$$xx]min=$$\frac { 10 } { 3 }$$min

Thus, I and II both are necessary to get the answer.

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