Time and Work Questions

FACTS  AND  FORMULAE  FOR  TIME  AND  WORK  QUESTIONS

 

 

1. If A can do a piece of work in n days, then A's 1 day's work =

2. If A’s 1 day's work =, then A can finish the work in n days.

 

3. A is thrice as good a workman as B, then:

Ratio of work done by A and B = 3 : 1.

Ratio of times taken by A and B to finish a work = 1 : 3.

 

NOTE : 

Hence, 

 

Whole work is always considered as 1, in terms of fraction and 100% , in terms of percentage.

In general, number of day's or hours = 

Q:

A is thrice efficient as B and C is twice as efficient as B. what is the ratio of number of days taken by A,B and C, when they work individually?

A) 2:6:3 B) 2:3:6
C) 1:2:3 D) 3:1:2
 
Answer & Explanation Answer: A) 2:6:3

Explanation:

                                                       A    :    B    :    C

Ratio of efficiency                    3     :    1    :    2

Ratio of No.of days               \inline \fn_jvn \left \{ \inline \fn_jvn \frac{1}{3}     :    \inline \fn_jvn \frac{1}{1}    :   \inline \fn_jvn \frac{1}{2}  \inline \fn_jvn \left \right \}

     or                                              2    :    6    :    3

Hence A is correct.     \inline \fn_jvn \left [ \because Time \prec \frac{1}{Eficiency} \right ]

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10 4263
Q:

(x-2) men can do a piece of work in x days and (x+7) men can do 75% of the same work in (x-10)days. Then in how many days can (x+10) men finish the work?

A) 27 days B) 12 days
C) 25 days D) 18 days
 
Answer & Explanation Answer: B) 12 days

Explanation:

\inline \fn_jvn \frac{3}{4}\times (x-2)x=(x+7)(x-10)

\inline \fn_jvn \Rightarrow    \inline \fn_jvn x^{2}-6x-280=0 

\inline \fn_jvn \Rightarrow    x= 20   and   x=-14

so, the acceptable values is x=20

\inline \fn_jvn \therefore Total work = \inline \fn_jvn (x-2)\times x = 18 x 20 =360 unit

Now   360 = 30 x k          \inline \fn_jvn \because (30=20+10)

\inline \fn_jvn \Rightarrow  k=12 days

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10 4178
Q:

A, B and C can complete a piece of work in 24,6 and 12 days respectively.Working together, they will complete the same work in:

A) 1/24 days B) 7/24 days
C) 24/7 days D) 4 days
 
Answer & Explanation Answer: C) 24/7 days

Explanation:

(A+B+C)'s 1 day's work =\inline {\color{Black}\left ( \frac{1}{24}+\frac{1}{6}+\frac{1}{12} \right )=\frac{7}{24}}

so, A,B and C together will complete the work in 24/7 days.

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9 3989
Q:

The ratio of efficiency of A is to C is 5:3. The ratio of number of days taken by B is to C is 2:3. A takes 6 days less than C, when A and C completes the work individually. B and C started the work and left after 2 days. The number of days taken by A to finish the remaining work is:

A) 4.5 B) 5
C) 6 D) 9 1/3
 
Answer & Explanation Answer: C) 6

Explanation:

                                A     :    B    :    C

Efficiency     \inline \fn_jvn \rightarrow         10    :    9    :     6

No of days   \inline \fn_jvn \rightarrow         9x    :  10x   :    15x

\inline \fn_jvn \Rightarrow       15x-9x = 6

\inline \fn_jvn \therefore             x = 1

Number of days taken b A = 9

Number of days taken by B= 10

Number of days taken by C = 15

work done by B and C in initial 2 days = \inline \fn_jvn \frac{2\times 1}{6} = \inline \fn_jvn \frac{1}{3}

           rest work =\inline \fn_jvn \frac{2}{3}

Number of days required by A to finish \inline \fn_jvn \frac{2}{3} work = \inline \fn_jvn \frac{2/3}{1/9} = 6 days

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17 3851
Q:

Pipe A can fill the tank in 4 hours,while pipe B can fill it in 6 hours working separately.pipe C can empty whole the tank in 4 hours. He opened the pipe A and B simultaneously to fill the empty tank. He wanted to adjust his alarm so that he could open the pipe C when it was half-filled, but he mistakenly adjusted his alarm at a time when his tank would be 3/4th filled. what is the time difference between both the cases, to fill the tank fully:

A) 48 min B) 54 min
C) 30 min D) none of these
 
Answer & Explanation Answer: B) 54 min

Explanation:

In ideal Case:

         Time taken to fill the half tank by A and B = \inline \fn_jvn \frac{50}{41.66} =\inline \fn_jvn \frac{6}{5} hours

         Time taken by A,B and C to fill rest half of the tank =\inline \fn_jvn \frac{50}{16.66} = 3 hours

         Total time = \inline \fn_jvn \frac{6}{5}+3 = 4 hours 12 min

In second case:

         Time taken to fill \inline \fn_jvn \frac{3}{4} tank by A and B =\inline \fn_jvn \frac{75}{41.66}=\frac{9}{5} hours

         Time taken by A,B and C to fill rest \inline \fn_jvn \frac{1}{4} tank = \inline \fn_jvn \frac{25}{16.66}=\frac{3}{2} hours

         Total time =\inline \fn_jvn \frac{9}{5}+\frac{3}{2} =3 hours 18 min

Therefore , difference in time = 54 minutes

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