Time and Work
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Q.

39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?

 A.

10

 B.

13

 C.

14

 D.

15

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Solution:
Option(B) is correct

Let's calculate how much time it takes to repair the road if just 1 person were working on it.

$5$ hours a day for $12$ days makes it $60$ hours per person.

$39$ people working $60$ hours each makes it $39×60=2340$ hours in total.


Now we have $30$ people working 6 hours a day

That means $30×6=180$ hours are spent each day.

We need a total of $2340$ hours. With $180$ hours every day, that's going to take \(\dfrac{2340}{180}=13\text{ days}\)

Edit: For further analysis and general conclusion, check comment by Chirag Goyal.


(10) Comment(s)


Chirag Goyal
 ()

Formula given by Rupesh shows that work done in both the conditions is same

More the $\text{No. of Persons(M)}$ Less the $\text{No. of Days(D)}$ and

More the $\text{No. of Persons(M)}$ Less the $\text{No. of Working Hours(T)}$ Need to complete Certain Work.

i.e. $\text{M}\propto\dfrac{1}{D} ; \text{M}\propto\dfrac{1}{T}$

$\Rightarrow M\propto \dfrac{1}{D\times T}$

So

$M_1 \times D_1 \times T1 = M_2 \times D_2 \times T_2$


Chetan
 ()

Above Explained Formula is known as $\bf{Chain\ Rule}$

Thank for this clear cut $\bf{Explanation}$


Vaibhaw
 ()

I think, 13 is the right ans as $\dfrac{39*12*5}{30*6}$


Shreya
 ()

That is good for every question


Riya
 ()

I am also getting 13 as the answer and not 9.


Shireesh
 ()

Can you show your calculation, since I am getting 13 as the final answer.


Rupesh Kumar Singh
 ()

$M_1 \times D_1 \times T1 = M_2 \times D_2 \times T_2$

$39 \times 12 \times 5=30 \times 6 \times x $

$X=\dfrac{39 \times 12 \times 5}{30 \times 6}$

$X=9$


Rakesh
 ()

Well, your Approach is right (same as the question), I believe you are making calculation mistake.

$$X=\dfrac{39*12*5}{30*6}=13$$

and not $X=9$

Poonam Pipaliya
 ()

but how can we directly take this..???

is there any particular formula..??..!!

Rajesh
 ()

No Poonam there is no particular formula.

Since it is asked in the question to complete the SAME JOB, total working hours in both the scenarios have been equated, simple basic mathematics logic :)