Time and Work Questions

Q:

A can do a piece of work in 10 days, B in 15 days. They work together for 5 days, the rest of the work is finished by C in two more days. If they get Rs. 3000 as wages for the whole work, what are the daily wages of A, B and C respectively (in Rs):

A) 200, 250, 300 B) 300, 200, 250
C) 200, 300, 400 D) None of these
 
Answer & Explanation Answer: B) 300, 200, 250

Explanation:

A's 5 days work = 50% 

B's 5 days work = 33.33%

C's 2 days work = 16.66%          [100- (50+33.33)]

Ratio of contribution of work of A, B and C = 

                                                               = 3 : 2 : 1

 

A's total share = Rs. 1500

B's total share = Rs. 1000

C's total share = Rs. 500

 

A's one day's earning = Rs.300

B's one day's earning = Rs.200

C's one day's earning = Rs.250

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Q:

12 men can complete a work in 8 days. 16 women can complete the same work in 12 days. 8 men and 8 women started working  and worked for 6 days. How many more men are to be added to complete the remaining work in 1 day?

A) 8 B) 12
C) 16 D) 24
 
Answer & Explanation Answer: B) 12

Explanation:

1 man's 1 day work =\inline {\color{Black}\frac{1}{96} } ; 1 woman's 1 day work =\inline {\color{Black}\frac{1}{192} }

work done in 6 days= \inline {\color{Black}6(\frac{8}{96}+\frac{8}{192}) =(6\times \frac{1}{8})=\frac{3}{4}}

Remaining work =\inline {\color{Black}(1-\frac{3}{4})=\frac{1}{4}}

(8 men +8 women)'s 1 day work =\inline {\color{Black}1(\frac{8}{96}+\frac{8}{192})}=\inline {\color{Black}\frac{1}{8}}

Remaining work=\inline {\color{Black}(\frac{1}{4}-\frac{1}{8})=\frac{1}{8}}

\inline {\color{Black}\frac{1}{96}} work is done in 1 day by 1 man

\inline {\color{Black}\therefore }\inline {\color{Black}\frac{1}{8}} work will be done in 1 day by \inline {\color{Black}(96\times \frac{1}{8})=12} men

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28 5401
Q:

Relation Between Efficiency and Time

A is twice as good a workman as B and is therefore able to finish a piece of work in 30 days less than B.In how many days they can complee the whole work; working together?

Answer

Sol:       Ratio of efficiency = 2:1 (A:B)


       Ratio of required time = 1:2 (A:B)       \inline \fn_jvn \Rightarrow x:2x


       but    2x-x=30  


       \inline \fn_jvn \Rightarrow  x= 30  and  2x= 60


       Now   efficiency of A =3.33%  and efficiency of B =1.66%


       Combined efficiency of A and B together = 5%


       \inline \fn_jvn \therefore time required by A and B working together to finish the work = \inline \fn_jvn \frac{100}{5} = 20 days


 


 


Note:      Efficiency \inline \fn_jvn \prec \inline \fn_jvn \frac{1}{number\: of \: time\: units}


             \inline \fn_jvn \therefore Efficiency \inline \fn_jvn \times  time = Constant Work


             Hence, Required time = \inline \fn_jvn \frac{work}{efficiency}


whole work is always cosidered as 1, in terms of fraction and 100%, in terms of percentage.


In, general no.of days or hours = \inline \fn_jvn \frac{100}{efficiency}      

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Q:

A can do a certain work in the same time in which B and C together can do it.If A and B together could do it in 20 days and C alone in 60 days ,then B alone could do it in:

A) 20days B) 40 days
C) 50 days D) 60 days
 
Answer & Explanation Answer: D) 60 days

Explanation:

(A+B)'s 1 day's work=1/20

C's 1 day work=1/60

(A+B+C)'s 1 day's work=\inline {\color{Black} \left ( \frac{1}{20} + \frac{1}{60}\right )=\frac{4}{60}=\frac{1}{15}}

Also A's 1 day's work =(B+C)'s 1 day's work

\inline {\color{Black} \therefore } we get: 2 * (A's 1 day 's work)=1/15

=>A's 1 day's work=1/30

\inline {\color{Black} \therefore } B's 1 day's work= \inline {\color{Black} \left ( \frac{1}{20} -\frac{1}{30}\right )=\frac{1}{60}}

So, B alone could do the work in 60 days.

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Q:

A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 4 days before the completion of the work. In how many days was the work completed?

A) 11 days B) 12 days
C) 13 days D) 14 days
 
Answer & Explanation Answer: A) 11 days

Explanation:

One day's work of A, B and C = (1/24 + 1/30 + 1/40) = 1/10

C leaves 4 days before completion of the work, which means only A and B work during the last 4 days.

Work done by A and B together in the last 4 days = 4 (1/24 + 1/30) = 3/10

Remaining Work = 7/10, which was done by A,B and C in the initial number of days. 

Number of days required for this initial work = 7 days.

Thus, the total numbers of days required = 4 + 7 = 11 days.

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