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# Time and Work Questions for IBPS PO Prelims

Question 1: A man and a woman, working together can do a work in 66 days. The ratio of their working efficiencies is 3 : 2. In how many days 6 men and 2 women working together can do the same work?

a) 18

b) 15

c) 14

d) 12

Solution:

Let the total work be 330 units.

Efficiency of a man and a woman together = $\frac{330}{66}$ = 5 units/day

The ratio of the working efficiencies of man and woman is 3 : 2.

Efficiency of a man = 3 units/day

Efficiency of a woman = 2 units/day

Efficiency of 6 men and 2 women together = (6 x 3) + (2 x 2) = 22 units/day

Time required for 6 men and 2 women together to complete the work = $\frac{330}{22}$ = 15 days

Hence, the correct answer is Option B

Question 2: A and B can do certain work in 18 days and 30 days,respectively. They work together for 5 days. C alone completes the remaining work in 15 days. A and C together can complete $\frac{5}{6}$th part of the same work in:

a) 6 days

b) 8 days

c) 9 days

d) 5 days

Solution:

Let the total work = 360 units

Efficiency of A = $\frac{360}{18}$ = 20 units/day

Efficiency of B = $\frac{360}{30}$ = 12 units/day

A and B worked together for 5 days.

Work done by A and B together in 5 days = 5 x (20 + 12) = 160 units

Remaining work = 360 – 160 = 200 units

C alone completes the remaining work in 15 days.

Efficiency of C = $\frac{200}{15}$ = $\frac{40}{3}$ units/day

Efficiency of A and C together = 20 + $\frac{40}{3}$ = $\frac{100}{3}$ units/day

$\frac{5}{6}$th of the total work = $\frac{5}{6}\times$360 = 300 units

Number of days required for A and C together to complete $\frac{5}{6}$th of work = $\frac{300}{\frac{100}{3}}$

= $\frac{300\times3}{100}$

= 9 days

Hence, the correct answer is Option C

Question 3: A can complete a work in $11\frac{1}{2}$ days. B is 25% more efficient than A and C is 50% less efficient than B. Working together A, B and C will complete the same work

a) 5 days

b) 4 days

c) 3 days

d) 8 days

Solution:

Let the total work = 460 units

A can complete a work in $11\frac{1}{2}$ days.

Efficiency of A = $\frac{460}{\frac{23}{2}}$ = 40 units/day

B is 25% more efficient than A.

Efficiency of B = $\frac{125}{100}\times40$ = 50 units/day

C is 50% less efficient than B.

Efficiency of C = $\frac{50}{100}\times50$ = 25 units/day

Efficiency of A, B and C together = 40 + 50 + 25 = 115 units/day

Number of days required for A, B and C together to complete the work = $\frac{460}{115}$ = 4 days

Hence, the correct answer is Option B

Question 4: To do a certain work, efficiencies of A and B are in the ratio 7:5. Working together, they can complete the work in $17\frac{1}{2}$ days. In how many days, will B alone complete 50% of the same work?

a) 42

b) 21

c) 15

d) 30

Solution:

Let the total work = 700 units

Efficiencies of A and B are in the ratio 7:5.

Let the efficiency of A and B are 7p and 5p respectively.

Efficiencies of A and B together = 7p + 5p = 12p units/day

Working together, they can complete the work in $17\frac{1}{2}$ days.

$\frac{700}{12p}$ = $17\frac{1}{2}$

$\frac{700}{12p}$ = $\frac{35}{2}$

p = $\frac{10}{3}$

Efficiency of B = 5p = $\frac{50}{3}$ units/day

Number of days required for B alone complete 50% of the same work = $\frac{350}{\frac{50}{3}}$

= $\frac{350\times3}{50}$

= 21 days

Hence, the correct answer is Option B

Question 5: A is twice as good a workman as B and together they finish a piece of work in 22 days. In how many days will A alone finish the same work?

a) 30 days

b) 44 days

c) 33 days

d) 11 days

Solution:

Let the total work = W

A is twice as good a workman as B

Let the number of days required for A alone to complete the work = a

$\Rightarrow$ Number of days required for B alone to complete the work = 2a

Work done by A in 1 day = $\frac{W}{a}$

Work done by B in 1 day = $\frac{W}{2a}$

Given, A and B together finish the work in 22 days

$\Rightarrow$  Work done by A and B together in 1 day = $\frac{W}{22}$

$\Rightarrow$  $\frac{W}{a}$ + $\frac{W}{2a}$ = $\frac{W}{22}$

$\Rightarrow$  $\frac{3}{2a}$ = $\frac{1}{22}$

$\Rightarrow$   a = 33

$\therefore\$Number of days required for A alone to complete the work = 33 days

Hence, the correct answer is Option C

Question 6: A and B together can complete a piece of work in 15 days. B and C together can do it in 24 days. If A is twice as good a workman as C, then in how many days can B alone complete the work?

a) 60 days

b) 40 days

c) 52 days

d) 45 days

Solution:

Let the total work = W

Given, A is twice as good a workman as C

Let the number of days required for A alone to complete the work = a

$\Rightarrow$ Number of days required for C alone to complete the work = 2a

Let the number of days required for B alone to complete the work = b

Work done by B in 1 day = $\frac{W}{b}$

Work done by A in 1 day = $\frac{W}{a}$

Work done by C in 1 day = $\frac{W}{2a}$

A and B together can complete a piece of work in 15 days

$\Rightarrow$  Work done by A and B together in 1 day = $\frac{W}{15}$

$\Rightarrow$  $\frac{W}{a}$ + $\frac{W}{b}$ = $\frac{W}{15}$

$\Rightarrow$  $\frac{1}{a}$ = $\frac{1}{15}$ – $\frac{1}{b}$ …………(1)

B and C together can complete the work in 24 days

$\Rightarrow$  Work done by B and C together in 1 day = $\frac{W}{24}$

$\Rightarrow$  $\frac{W}{b}$ + $\frac{W}{2a}$ = $\frac{W}{24}$

$\Rightarrow$  $\frac{1}{b}$ + $\frac{1}{2a}$ = $\frac{1}{24}$

$\Rightarrow$  $\frac{1}{b}$ + $\frac{1}{2}\left[\frac{1}{15}-\frac{1}{b}\right]$ = $\frac{1}{24}$   [From (1)]

$\Rightarrow$  $\frac{1}{2b}$ = $\frac{1}{24}$ – $\frac{1}{30}$

$\Rightarrow$  $\frac{1}{2b}$ = $\frac{5-4}{120}$

$\Rightarrow$  $\frac{1}{b}$ = $\frac{1}{60}$

$\Rightarrow$  b = 60

$\therefore\$Number of days required for B alone to complete the work = 60 days

Hence, the correct answer is Option A

Question 7: 10 men working 5 hours/day earn ₹300. How much money will 15 men working 10 hours/day earn?

a) ₹ 800

b) ₹ 600

c) ₹ 650

d) ₹ 900

Solution:

Given, 10 men working 5 hours/day earn ₹300

1 man working 5 hours/day earn ₹30

15 men working 5 hours/day  earn 30 x 15 = ₹450

$\Rightarrow$  15 men working 10 hours/day earn 450 x 2 = ₹900

Question 8: A and B working together can do 30% of the work in 6 days. B alone can do the same work in 25 days. How long will A alone take to complete the same work?

a) 100 days

b) 60 days

c) 75 days

d) 80 days

Solution:

Given, A and B working together can do 30% of the work in 6 days

$\Rightarrow$ A and B working together can do 10% of the work in 2 days

$\Rightarrow$ A and B working together can do 100% of the work in 20 days

Let the total work = W

Work done by A and B together in 1 day = $\frac{W}{20}$

B alone can do the same work in 25 days

Work done by B alone in 1 day = $\frac{W}{25}$

$\Rightarrow$ Work done by A alone in 1 day = $\frac{W}{20}-\frac{W}{25}=\frac{5W-4W}{100}=\frac{W}{100}$

$\therefore\$Number of days required for A alone to complete the work = 100 days

Hence, the correct answer is Option A

Question 9: P can work thrice as fast as Q. Working independently, Q can complete a task in 24 days. In how many days can P and Q together finish the same task?

a) 4

b) 5

c) 8

d) 6

Solution:

Number of days required for Q to complete the task = 24 days

P can work thrice as fast as Q

$\Rightarrow$  Number of days required for P to complete the task = $\frac{24}{3}$ days = 8 days

Let the total work be W

Work done by P in 1 day = $\frac{W}{8}$

Work done by Q in 1 day = $\frac{W}{24}$

$\Rightarrow$ Work done by both P and Q in 1 day = $\frac{W}{8}+\frac{W}{24}=\frac{3W+W}{24}=\frac{W}{6}$

$\therefore\$Number of days required for both P and Q to complete the task = $\frac{W}{\frac{W}{6}}$ = 6 days

Hence, the correct answer is Option D

Question 10: 25 men can complete a task in 16 days. Four days after they started working, 5 more men, with equal workmanship, joined them. How many days will be needed by all to complete the remaining task?

a) 10 days

b) 12 days

c) 15 days

d) 18 days

Solution:

Let the total work = W

25 men can complete the task in 16 days

$=$>  Number of days required for 25 men to complete the work = 16 days

$=$>  Work done by 25 men in 1 day = $\frac{W}{16}$

$=$>  Work done by 25 men in 4 days =$4\times\frac{W}{16}=\frac{W}{4}$

$\therefore\$Remaining work = $W-\frac{W}{4}=\frac{3W}{4}\$

Let the number of days required for 30 men to complete remaining work = $d_2$ days

We know that $\frac{M_1d_1}{W_1}=\frac{M_2d_2}{W_2}$

$=$>  $\frac{25\times16}{W}=\frac{30\times d_2}{\frac{3W}{4}}$

$=$>  $\frac{25\times16}{W}=\frac{30\times d_2\times4}{3W}$

$=$>  $d_2=10$ days

$\therefore\$The number of days required for 30 men to complete remaining work = 10 days

Hence, the correct answer is Option A

Question 11: Smith and Ajit can complete a task in 12 days and 18 days, respectively. If they work together on the task for 4 days, then the fraction of the task that will be left is:

a) $\frac{4}{9}$

b) $\frac{1}{9}$

c) $\frac{2}{9}$

d) $\frac{5}{9}$

Solution:

Number of days required for Smith to complete the task = 12 days

$=$>  Part of the task completed by Smith in 1 day = $\frac{T}{12}$

Number of days required for Ajit to complete the task = 18 days

$=$>  Part of the task completed by Ajit in 1 day = $\frac{T}{18}$

Part of the task completed by both Smith and Ajit in 1 day = $\frac{T}{12}+\frac{T}{18}=\frac{3T+2T}{36}=\frac{5T}{36}$

Part of the task completed by both Smith and Ajit in 4 days = $4\times\frac{5T}{36}=\frac{20T}{36}$

$\therefore\$Fraction of the task left = $\text{T}-\frac{20T}{36}=\frac{36T-20T}{36}=\frac{16T}{36}=\frac{4}{9}\text{T}$

Hence, the correct answer is Option A

Question 12: P and Q can finish a work in 10 days and 5 days, respectively. Q worked for 2 days and left the job. In how many days can P alone finish the remaining work?

a) 6 days

b) 4 days

c) 10 days

d) 8 days

Solution:

Let the total work be W

Number of required for P to finish the work = 10 days

$=$>  Work done by P in 1 day = $\frac{W}{10}$

Number of required for Q to finish the work = 5 days

$=$> Work done by Q in 1 day = $\frac{W}{5}$

$=$> Work done by Q in 2 days = $\frac{2W}{5}$

Remaining work = $\text{W}-\frac{2W}{5}$ = $\frac{3W}{5}$

$\therefore\$Number of days required for P to finish the remaining work = $\frac{\frac{3W}{5}}{\frac{W}{10}}$ = $\frac{3W}{5}\times\frac{10}{W}$ = 6 days

Hence, the correct answer is Option A

Question 13: X and Y together can finish a piece of work in 15 days, while Y alone can finish it in 40 days. X alone can finish the work in:

a) 24 days

b) 26 days

c) 25 days

d) 23 days

Solution:

Let the total work = W

Number of days in which X and Y together finish the work = 15 days

$=$>  Work done by X and Y together in 1 day = $\frac{W}{15}$

Number of days in which Y alone finish the work = 40 days

$=$>  Work done by Y alone in 1 day = $\frac{W}{40}$

$=$>  Work done by X alone in 1 day = $\frac{W}{15}-\frac{W}{40}=\frac{5W}{120}=\frac{W}{24}$

$\therefore\$Number of days in which X alone finish the work = $\frac{W}{\frac{W}{24}}=24$ days

Hence, the correct answer is Option A

Question 14: Raju can finish a piece of work in 20 days. He worked at it for 5 days and then Jakob alone finished the remaining work in 15 days. In how many days can both finish it together?

a) 20 days

b) 12 days

c) 10 days

d) 16 days

Solution:

Let the total work = W

Number of days required for Raju to complete the work = 20 days

$=$>  Work done by Raju in 1 day = $\frac{W}{20}$

$=$>  Work done by Raju in 5 days = $\frac{5W}{20}=\frac{W}{4}$

Remaining work = $W-\frac{W}{4}=\frac{3W}{4}$

$\therefore\$Work done by Jakob in 15 days = $\frac{3W}{4}$

$=$>  Work done by Jakob in 1 day = $\frac{3W}{60}=\frac{W}{20}$

$=$>  Work done by Raju and Jakob in 1 day = $\frac{W}{20}+\frac{W}{20}=\frac{2W}{20}=\frac{W}{10}$

$=$>  Number of days required for both Raju and Jakob to complete the work = $\frac{W}{\frac{W}{10}}=10$ days

Hence, the correct answer is Option C

Question 15: A and B separately can build a wall in 12 and 16 days, respectively. If they work for 1 day alternatively, starting with A, in how many days will the wall be built?

a) $6 \frac{3}{4}$ days

b) $12 \frac{2}{3}$ days

c) $13 \frac{2}{3}$ days

d) $7 \frac{2}{3}$ days

Solution:

Let the total work = W

Number of days required for A to build the wall = 12 days

$=$>  Work done by A in 1 day = $\frac{W}{12}$

Number of days required for B to build the wall = 16 days

$=$>  Work done by B in 1 day = $\frac{W}{16}$

Work done by both A and B in 2 days working alternatively for 1 day = $\frac{W}{12}+\frac{W}{16}=\frac{7W}{48}$

$=$>  Work done by both A and B in 12 days working alternatively for 1 day = $\frac{7W}{48}\times\frac{12}{2}=\frac{7W}{8}$

Remaining work after 12 days = $W-\frac{7W}{8}=\frac{W}{8}$

Remaining work after A working on the 13th day = $\frac{W}{8}-\frac{W}{12}=\frac{W}{24}$

$=$>  The remaining work $\frac{W}{24}$ will be completed by B

Number of days required for B to complete $\frac{W}{24}$ = $\frac{\frac{W}{24}}{\frac{W}{16}}=\frac{2}{3}$ day

$\therefore\$Number of days required to complete the total work = 12 + 1 + $\frac{2}{3}$ = $13 \frac{2}{3}$ days

Hence, the correct answer is Option C

Question 16: Ramu works 4 times as fast as Somu. If Somu can complete a work in 20 days independently, then the number of days in which Ramu and Somu together can complete the work is:

a) 4 days

b) 5 days

c) 3 days

d) 6 days

Solution:

Number of days required for Somu to complete work = 20 days

Ramu works 4 times as fast as Somu

$=$> Number of days required for Ramu to complete work = $\frac{20}{4}=5$ days

Let the Total Work = W

Work done by Ramu in 1 day = $\frac{W}{5}$

Work done by Somu in 1 day = $\frac{W}{20}$

Work done by Ramu and Somu in 1 day = $\frac{W}{5}+\frac{W}{20}=\frac{5W}{20}=\frac{W}{4}$

Number of days required for both Ramu and Somu together to complete work = $\frac{W}{\frac{W}{4}}=4$ days

Hence, the correct answer is Option A

Question 17: If 27 people, working 8 hours a day, can complete a task in 12 days, then in how many days will 18 people finish the task, working 9 hours a day?

a) 15 days

b) 20 days

c) 16 days

d) 18 days

Solution:

Given,

27 people working 8 hours a day can complete the task in 12 days

$=$>  $M_1=27$,  $d_1=12$,  $h_1=8$

Let 18 people working 9 hours a day can complete the task in $d_2$ days

$=$>  $M_2=18$,  $h_2=9$

Let the total work = W

we know that $\frac{M_1\times d_1\times h_1}{W_1}=\frac{M_2\times d_2\times h_2}{W_2}$

$=$>  $\frac{27\times12\times8}{W}=\frac{18\times d_2\times9}{W}$

$=$>  $d_2=$ 16 days

Hence, the correct answer is Option C

Question 18: A can finish a piece of work in a certain number of days. B takes 45% more number of days to finish the same work independently. They worked together for 58 days and then the remaining work was done by B alone in 29 days. In how many days could A have completed the work, had he worked alone?

a) 110 days

b) 118 days

c) 98 days

d) 120 days

Solution:

Let the number of days required for A alone to complete the work = 100a

$=$>  Number of days required for B alone to complete the work = 145a

Let the total work = W

Work done by A in 1 day = $\frac{W}{100a}$

Work done by B in 1 day = $\frac{W}{145a}$

Work done by A and B in 1 day = $\frac{W}{100a}+\frac{W}{145a}=\frac{245W}{14500a}=\frac{49W}{2900a}$

Work done by A and B in 58 days$=58\times\frac{49W}{2900a}=\frac{49W}{50a}$

Remaining work $=W-\frac{49W}{50a}$

Remaining work is completed by B in 29 days

$=$>  $W-\frac{49W}{50a}=\frac{29W}{145a}$

$=$>  $W=\frac{29W}{145a}+\frac{49W}{50a}$

$=$>  $W=\frac{1450W+7105W}{145\times50\times a}$

$=$>  $W=\frac{8555W}{145\times50\times a}$

$=$>  $W=\frac{59W}{50a}$

$=$>  $50a=59$

$=$>  $100a=118$

$\therefore\$Number of days required for A alone to complete the work = 100a = 118 days

Hence, the correct answer is Option B

Question 19: Shyam can complete a task in 12 days by working 10 hours a day. How many hours a day should he work to complete the task in 8 days?

a) 12

b) 15

c) 16

d) 14

Solution:

Given, Shyam can complete the task in 12 days working 10 hours a day

$=$> Total time required for Shyam to complete the task = 12 x 10 = 120 hours

$\therefore\$ Number of hours Shyam should work in a day to complete task in 8 days = $\frac{120}{8}$ = 15 hours

Hence, the correct answer is Option B

Question 20: To complete a certain task, X is 40 % more efficient than Y, and Z is 40% less efficient than Y. Working together, they can complete the task in 21 days. Y and Z together worked for 35 days. The remaining work will be completed by X alone in:

a) 8 days

b) 4 days

c) 6 days

d) 5 days

Solution:

Efficiency of X = 140% of Y = 1.4Y

Efficiency of Z = 60% of Y = 0.6Y

Efficiency of X, Y and Z = 1.4 : 1 : 0.6 = 7 : 5 : 3

They can complete the task in 21 days so,

Total work = sum of efficiency ratio $\times times = (7 + 5 + 3) \times 21 = 315$

Y and Z together worked for 35 days so,

Work done by Y and Z = (5 + 3) $\times$ 35 = 280

Remaining work = 315 – 280 = 35

Remaining work complete by X = work/efficiency = 35/7 = 5 days