# 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

Explanation:

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

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

B's 1 day's work=1/18

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

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

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

Explanation:

A     :    B    :    C

Efficiency     $\inline&space;\fn_jvn&space;\rightarrow$         10    :    9    :     6

No of days   $\inline&space;\fn_jvn&space;\rightarrow$         9x    :  10x   :    15x

$\inline&space;\fn_jvn&space;\Rightarrow$       15x-9x = 6

$\inline&space;\fn_jvn&space;\therefore$             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 = $\inline&space;\fn_jvn&space;\frac{2\times&space;1}{6}$ = $\inline&space;\fn_jvn&space;\frac{1}{3}$

rest work =$\inline&space;\fn_jvn&space;\frac{2}{3}$

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

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

Explanation:

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

$\inline&space;\fn_jvn&space;\Rightarrow$    $\inline&space;\fn_jvn&space;x^{2}-6x-280=0$

$\inline&space;\fn_jvn&space;\Rightarrow$    x= 20   and   x=-14

so, the acceptable values is x=20

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

Now   360 = 30 x k          $\inline&space;\fn_jvn&space;\because&space;(30=20+10)$

$\inline&space;\fn_jvn&space;\Rightarrow$  k=12 days

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

Explanation:

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

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

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

Explanation:

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

B + C =50%

$\inline&space;\fn_jvn&space;\Rightarrow$ B= 20%     A= 50%        and   C=30%

Hence A is most efficient