Time and Work Questions

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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6 1923
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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11 1833
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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5 1815
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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3 1758
Q:

When A, B and C are deployed for a task , A and B together do 70% of the work and B and C together do 50% of the work. who is most efficient?

A) A B) B
C) C D) can't be determined
 
Answer & Explanation Answer: A) A

Explanation:

A + B= 70%            \inline \fn_jvn \begin{bmatrix} \therefore (A+B)+(B+c)-(A+B+C)=B\\ 70+50-100=20 \end{bmatrix}

B + C =50% 

 

          \inline \fn_jvn \Rightarrow B= 20%     A= 50%        and   C=30%

Hence A is most efficient

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