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Chain Rule Questions and Answers

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21.

36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work ?

Answer: A

Less Men, means more Days {Indirect Proportion}

Let the number of days be x then,

27 : 36 :: 18 : x


[Please pay attention, we have written 27 : 36 rather than 36 : 27, in indirect proportion, if you get it then chain rule is clear to you :)]                                

=>27x = 36 * 18

=> x = 24

 So 24 days will be required to get work done by 27 men.

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22.

Some persons can do a piece of work in 12 days. Two times the number of such persons will do half of that work in

Answer: D

Let x men can do the in 12 days and the required number of days be z

 

More men, Less days     [Indirect Proportion]

 

Less work, Less days     [Direct Proportion  ]

 men2x:xwork1:12 :: 12 : z

∴2x×1×z=x×12×12

 ⇒z=3

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23.

A certain number of men can finish a piece of work in 100 days. If there were 10 men less, it would take 10 days more for the work to be finished. How many men were there originally?

   
   

Answer: D

The total work in man-days is fixed.

\[ 100M = 110(M - 10) \]

\[ 100M = 110M - 1100 \quad\Longrightarrow\quad 10M = 1100 \]

\[ M = 110 \]

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24.

A man can walk a certain distance at a uniform speed in 100 days. How long will it take him to cover twice the distance at half the normal speed?

Answer: E

Time is proportional to distance and inversely proportional to speed.

\[ t' = 100 \times 2 \times \frac{1}{1/2} = 100 \times 2 \times 2 \]

\[ = 400 \text{ days} \]

Doubling the distance doubles the time, and halving the speed doubles it again - the two effects compound.

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