Time and Work
Aptitude

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Q.

A work is done by three person A, B and C. A alone takes 10 hours to complete a single product but B and C working together takes 4 hours, for the completion of the same product.

If all of them worked together and completed 14 products, then how many hours have they worked?

 A.

20 hrs

 B.

28 hrs

 C.

40 hrs

 D.

54 hrs

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Solution:
Option(C) is correct

As given in the question,

\(\begin{align*} \dfrac{1}{A}&=10\\ \dfrac{1}{B}+\dfrac{1}{C}&=\dfrac{1}{4}\\ \dfrac{1}{B}+\dfrac{1}{C}+\dfrac{1}{A}&=\dfrac{7}{20} \end{align*}\)

In 20 hours, working together, they will complete 7 products. 

Thus, in 40 hours they will complete 14 products.

Edit: Thank you Abhishek Fauzdar for providing an alternate solution in the comments.

Edit 2: Here is yet another alternative solution by Dan.

Edit 3: For yet-yet another alternative solution, check comment by Karan Sharma.


(7) Comment(s)


RAHUL
 ()

As A work's =10 hr

AS B+C work's=4 hr

total work = L.C.M of 4 and 10 = 20 work for 1 product

SO,A work's for 1 hr =2 and B+C work's =5

Total work of A+B+C = 5 + 2 = 7

Total work's of 14 product = 14*20=280

Time Taken to complete 14 product work's = 280/7=40 hrs



Ramesh
 ()

wow such an easy method bro u really helped me with ur solution



Ramesh
 ()

wow such an easy method i want to learn from i am too weak in maths



Karan Sharma
 ()

$A$ takes $\dfrac{10h}{\text{product}}$, so for 14 product $A$ takes $140h$.

$B$ and $C$ together $(B+C)$ take $\dfrac{4h}{\text{product}}$, so togther will complete 14 products in $56h$.

So, $A+(B+C)$ is what we require.

Which is $\dfrac{1}{140}+\dfrac{1}{56}$

$=\textbf{40 hours}$



Dan
 ()

Amount of product produced by $A+B+C$ in 1 hour = $\dfrac{1}{10}+\dfrac{1}{4}=\dfrac{7}{20}$

If it takes 1 hour to complete only $\dfrac{7}{20}$ of one detail, then the amount of time spent on 1 whole detail is $\dfrac{20}{7}$.

So we get 2.85 spent by $A+B+C$ on one product.

We have 14 products then $14 \times 2.85=40$. 40 is the total amount of time spent.



NUR MOHAMMAD KHANDAKER
 ()

$A+B+C= \frac{1}{10}+\frac{1}{4}=\frac{14}{40}$ part to produce 1 product but reverse this fraction $\frac{40}{14}$ hours to produce 1 product so

1 product need $\frac{40}{14}$ hours

14 product need $\frac{40}{14}*14 = 40$ hours



Abhishek Fauzdar
 ()

A'S ONE HOUR WORK=10%

B+C 'S ONE HOUR WORK= 25%

A+B+C 'S ONE HOUR WORK =35%

THEREFORE 1400/35= 40 HOURS TO COMPLETE