Time and Work Questions

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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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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12 2203
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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7 2194
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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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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