# Time and Work Questions

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

Explanation:

2(A+B+C)'s 1 day work = $\inline&space;{\color{Black}\left&space;(&space;\frac{1}{30}+\frac{1}{24}+\frac{1}{20}&space;\right&space;)=\frac{15}{120}=\frac{1}{8}&space;}$

=>(A+B+C)'s  1 day's work=$\inline&space;{\color{Black}\frac{1}{16}&space;}$

work done by A,B and C in 10 days=$\inline&space;{\color{Black}\frac{10}{16}=&space;\frac{5}{8}}$

Remaining work=$\inline&space;{\color{Black}(1-\frac{5}{8})=&space;\frac{3}{8}}$

A's 1 day's work =$\inline&space;{\color{Black}(\frac{1}{16}-\frac{1}{24})=\frac{1}{48}}$

Now, $\inline&space;{\color{Black}\frac{1}{48}}$ work is done by A in 1 day.

So, $\inline&space;{\color{Black}\frac{3}{8}}$ work  wil be done by A in $\inline&space;{\color{Black}(48\times&space;\frac{3}{8})}$ = 18 days

4 2717
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

Explanation:

A    :    B    :    C

Ratio of efficiency                    3     :    1    :    2

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

or                                              2    :    6    :    3

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

10 2587
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

8 2501
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.

6 2436
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