Time and Work Questions

Q:

P can complete a work in 12 days working 8 hours a day.Q can complete the same work in 8 days working 10 hours a day. If both p and Q work together,working 8 hours a day,in how many days can they complete the work?

A) 60/11 B) 61/11
C) 71/11 D) 72/11
 
Answer & Explanation Answer: A) 60/11

Explanation:

P can complete the work in (12 * 8) hrs = 96 hrs

Q can complete the work in (8 * 10) hrs=80 hrs

\inline {\color{Black}\therefore } P's 1 hour work=1/96   and Q's 1 hour work= 1/80

(P+Q)'s 1 hour's work =\inline {\color{Black} \left ( \frac{1}{96}+\frac{1}{80} \right )} =\inline {\color{Black} \frac{11}{480}}

so both P and Q will finish the work in \inline {\color{Black} \frac{480}{11}} hrs

\inline {\color{Black} \therefore } Number of days of 8 hours each = \inline {\color{Black} \left ( \frac{480}{11} \times \frac{1}{8}\right )=\frac{60}{11}}

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9 3815
Q:

A works twice as fast as B.If  B can complete a work in 18 days independently,the number of days  in which A and B can together finish the work is:

A) 4 days B) 6 days
C) 8 days D) 10 days
 
Answer & Explanation Answer: B) 6 days

Explanation:

 Ratio of rates of working of A and B =2:1. So, ratio of times taken =1:2

\inline {\color{Black}\therefore }A's 1 day's work=1/9

   B's 1 day's work=1/18

(A+B)'s 1 day's work=\inline {\color{Black}(\frac{1}{9} +\frac{1}{18})=\frac{3}{18}=\frac{1}{6} }

so, A and B together can finish the work in 6 days

 

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8 3012
Q:

A can do a piece of work in 18 days, B in 27 days, C in 36 days. They start worked together . But only C work till the completion of work. A leaves 4 days and B leaves 6 days before the completion of work. In how many days work be completed?

Answer

Let the work be completed in x days


(x-4)days of A + (x-6)days of B + x days of C = 1


\inline \Rightarrow \inline \frac{x-4}{18}+\frac{x-6}{27}+\frac{x}{36}=1


\inline \Rightarrow \frac{13x-48}{108}=1


           x = 12


\inline \therefore Total time = 12 days


 

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7 2950
Q:

A Contractor employed a certain number of workers  to finish constructing a road in a certain scheduled time. Sometime later, when a part of work had been completed, he realised that the work would get delayed by three-fourth of the  scheduled time, so he at once doubled the no of workers and thus he managed to finish the road on the scheduled time. How much work he had been completed, before increasing the number of workers?

A) 10 % B) 14 2/7 %
C) 20 % D) Can't be determined
 
Answer & Explanation Answer: B) 14 2/7 %

Explanation:

Let he initially employed x workers which works for D days and he estimated 100 days for the whole work and then he doubled the worker for (100-D) days.

      D * x +(100- D) * 2x= 175x

       =>  D= 25 days

Now , the work done in 25 days = 25x

               Total work = 175x

therefore, workdone before increasing the no of workers = \frac{25x}{175x}\times 100=14\frac{2}{7} %

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17 2830
Q:

A and  B can do  a piece of work in 30 days , while  B and C can do the same work in 24 days and C and A in 20 days . They all work together for 10 days when B and C leave. How many days more will A take to finish  the work?

A) 18 days B) 24 days
C) 30 days D) 36 days
 
Answer & Explanation Answer: A) 18 days

Explanation:

2(A+B+C)'s 1 day work = \inline {\color{Black}\left ( \frac{1}{30}+\frac{1}{24}+\frac{1}{20} \right )=\frac{15}{120}=\frac{1}{8} }

=>(A+B+C)'s  1 day's work=\inline {\color{Black}\frac{1}{16} }

work done by A,B and C in 10 days=\inline {\color{Black}\frac{10}{16}= \frac{5}{8}}

Remaining work=\inline {\color{Black}(1-\frac{5}{8})= \frac{3}{8}}

A's 1 day's work =\inline {\color{Black}(\frac{1}{16}-\frac{1}{24})=\frac{1}{48}}

Now, \inline {\color{Black}\frac{1}{48}} work is done by A in 1 day.

So, \inline {\color{Black}\frac{3}{8}} work  wil be done by A in \inline {\color{Black}(48\times \frac{3}{8})} = 18 days

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