39 people 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
Last updated date: 27th Mar 2023
•
Total views: 306k
•
Views today: 2.82k
Answer
306k+ views
Hint: Use the unitary method to solve this question. Suppose the total amount of work would be ‘1’ (unity). Now, find the fraction of the amount done by 1 person in 1 working day with 1 hour a day to find the answer.
Complete step-by-step answer:
Let use the unitary method to calculate the part of work done by 1 person in one day and working in 1 hour by the following way:
Let us suppose the whole work as unity i.e. ‘1’.
So, 39 people in 12 days by working 5 hours a day are doing ‘1’ amount of 1 work.
So, 1 person in 12 days by working 5 hours in a day can do $'\dfrac{1}{39}'$ part of that work.
Hence, 1 person in 1 day by working 1 hour in a day can do $\dfrac{1}{39\times 12\times 5}$part of the work.
Now coming to the second condition of the problem, let us suppose 39 persons will complete the same work in ‘x’ days by working 6 hours a day.
So, 30 people in x days with 6 hours working in a day completes 1 work.
Hence, 1 person in 1 day with 1 hour working a day can complete the $\dfrac{1}{30\times x\times 6}$ part of the work.
Therefore, by using the both conditions, we get the same results i.e., part of working by 1 person in 1 day with 1 hour working. Hence, both should be equal.
So we get
$\Rightarrow$ $\dfrac{1}{30\times x\times 6}=\dfrac{1}{39\times 12\times 5}$
$\Rightarrow$ $30\times x\times 6=39\times 12\times 5$
$\begin{align}
& x=\dfrac{39\times 12\times 5}{30\times 6} \\
& x=\dfrac{39\times 2}{6}=\text{13 days} \\
\end{align}$
Hence, option (b) is the correct answer.
Note: One can use direct relation ${{M}_{1}}{{W}_{1}}{{D}_{1}}={{M}_{2}}{{W}_{2}}{{D}_{2}}$, where M is representing number of persons, W is representing working hours and D is representing number of days, ‘1’ and ‘2’ are used for two groups that complete the same work with ${{\text{M}}_{\text{1}}}{{\text{W}}_{\text{1}}}{{\text{D}}_{\text{1}}}\text{and}{{\text{M}}_{\text{2}}}{{\text{W}}_{\text{2}}}{{\text{D}}_{\text{2}}}$ features.
Hence, we can apply the given relation in these types of problems.
No need for formula if basics are clear for the chapter work and time. So, always think conceptually, you will be able to solve any problem from this chapter.
Complete step-by-step answer:
Let use the unitary method to calculate the part of work done by 1 person in one day and working in 1 hour by the following way:
Let us suppose the whole work as unity i.e. ‘1’.
So, 39 people in 12 days by working 5 hours a day are doing ‘1’ amount of 1 work.
So, 1 person in 12 days by working 5 hours in a day can do $'\dfrac{1}{39}'$ part of that work.
Hence, 1 person in 1 day by working 1 hour in a day can do $\dfrac{1}{39\times 12\times 5}$part of the work.
Now coming to the second condition of the problem, let us suppose 39 persons will complete the same work in ‘x’ days by working 6 hours a day.
So, 30 people in x days with 6 hours working in a day completes 1 work.
Hence, 1 person in 1 day with 1 hour working a day can complete the $\dfrac{1}{30\times x\times 6}$ part of the work.
Therefore, by using the both conditions, we get the same results i.e., part of working by 1 person in 1 day with 1 hour working. Hence, both should be equal.
So we get
$\Rightarrow$ $\dfrac{1}{30\times x\times 6}=\dfrac{1}{39\times 12\times 5}$
$\Rightarrow$ $30\times x\times 6=39\times 12\times 5$
$\begin{align}
& x=\dfrac{39\times 12\times 5}{30\times 6} \\
& x=\dfrac{39\times 2}{6}=\text{13 days} \\
\end{align}$
Hence, option (b) is the correct answer.
Note: One can use direct relation ${{M}_{1}}{{W}_{1}}{{D}_{1}}={{M}_{2}}{{W}_{2}}{{D}_{2}}$, where M is representing number of persons, W is representing working hours and D is representing number of days, ‘1’ and ‘2’ are used for two groups that complete the same work with ${{\text{M}}_{\text{1}}}{{\text{W}}_{\text{1}}}{{\text{D}}_{\text{1}}}\text{and}{{\text{M}}_{\text{2}}}{{\text{W}}_{\text{2}}}{{\text{D}}_{\text{2}}}$ features.
Hence, we can apply the given relation in these types of problems.
No need for formula if basics are clear for the chapter work and time. So, always think conceptually, you will be able to solve any problem from this chapter.
Recently Updated Pages
Paulings electronegativity values for elements are class 11 chemistry CBSE

For a particle executing simple harmonic motion the class 11 physics CBSE

Does Nichrome have high resistance class 12 physics CBSE

The function f satisfies the functional equation 3fleft class 12 maths JEE_Main

Write a letter to the Principal of your school to plead class 10 english CBSE

Look at the handout below Write a letter to the organizers class 11 english CBSE

Trending doubts
What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?
