Aptitude Discussion

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 |

**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.**

**Sourav Das**

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**Naina**

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A=10

B+C=4

LCM of 10&4=20

A=20/10=2

B+c=20/4=5

A+B+C=2+5=7

20/7*14=40 hrs

**RAHUL**

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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**

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

**Ramesh**

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

**Karan Sharma**

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$A$ 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**

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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**

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$A+B+C= \frac{1}{10}+\frac{1}{4}=\frac{14}{40}$ 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**

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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

1hr work of A =1/20

1hr work of B+C =1/4

1hr work of A+B+C =1/10 + 1/4 =7/20

Time taken by A+B+C in doing 1 work=1÷ 7/20= 20/7hrs

Therefore,time taken by A+B+C in doing 14 work=20/7 × 14 = 40hrs