# How To Solve Work And Time Questions Quickly

## How to Solve Work and Time Questions Quickly

When a duration of time (T) is required to complete a work (W) i.e. number of units of work done per unit time is called the rate of Work. Hence, Whenever some work is done and the total work itself can be taken as one unit.

### How to solve Work And Time questions

• Definition
Work: It is defined as the amount of job assigned or the amount of job actually done.
Time: Time is defined as the number of days or hours required to complete the task.

### Type 1: Calculate time taken or work completed by one, two or more workers

Question 1. Rohan and Mohan can paint a wall in 12 days together, Mohan and Sohan can paint the same wall in 15 days together and Rohan and Soham can paint that wall in 20 days together. In how many days Rohan alone can paint the wall?

Options

A. 20

B. 30

C. 40

D. 25

Solution:    Rohan + Mohan + Soham one day work = $\frac{1}{2}$ ($\frac{1}{12}$ + $\frac{1}{15}$ + $\frac{1}{20}$)

Rohan + Mohan + Soham one day work =$\frac{1}{10}$

Now, Rohan’s one day work =$\frac{1}{10}$$\frac{1}{15}$ = $\frac{1}{30}$

Therefore, Rohan alone will paint the wall in 30 days.

Correct option: B

Question 2.Mamta can alone complete a part of assignment in 8 days. Work done by Sunil alone in one day is half of the work done by Mamta alone in one day. In how many days can the assignment be completed, if Mamta and Sunil work together?

Options:

A. 5.33 days

B. 16 days

C. 24 days

D. 4 days

Solution:     Mamta can finish part of assignment in one day = $\frac{1}{8}$

Sunil can finish part of assignment in one day = $\frac{1}{16}$

Mamta + Sunil together finish part of assignment in one day = $\frac{1}{8}$ + $\frac{1}{16}$ = $\frac{3}{16}$

Therefore, together they will take $\frac{16}{3}$ days = 5.33 days.

Correct option: A

Question 3. Husband H and wife W can do a work in 24 days together. Husband can do the same job in 60 days alone. Then at what time wife can complete the same work alone?

Options:

A. 10

B. 20

C. 30

D. 40

Solution:     Wife’s one day work = $\frac{1}{24}$$\frac{1}{60}$ = $\frac{1}{40}$

Therefore, she will take 40 days.

Correct option: D

### Type 2:How To Solve Quickly Work and Time Questions when efficiency is given in percentage

Question 1. Jaya is twice as efficient as Maya. Jaya takes 30 days less than Maya to finish the work.  Calculate the time required to finish the work together.

Options:

A.40 days

B. 30 days

C. 20 days

D. 35 days

Solution:     Time required to complete the job together is given by

T = m × $\frac{D}{m^2 – 1}$

T = 2 × $\frac{30}{2^2 – 1}$

T =$\frac{60}{3}$

T= 20 days.

Correct option: C

Question 2. 6 students and 3 professionals can complete a task in 12 days by working 8 hours every day. In how much time will 12 professionals complete the same task by working 6 hours every day, if the efficiency of each student is twice that of a professionals?

Options:

A. 20 days

B. 10 days

C. 25 days

D. 15 days

Solution:    1 student= 2 professionals (as given in question, efficiency of each student is twice that of a professionals)

6 students = 12 professionals

As given

(6 students + 3 professionals) * 8 * 12 = 12 professionals * 6 * D

15 professionals * 8 * 12 = 12 girls * 6 * D

Correct option: A

Question 3. Rajat takes 6 days to complete the assignment whereas Jannat completes the same assignment in 12 days. In how much time they will complete the assignment together?

Options:

A. 2 days

B. 3 days

C. 4 days

D. 1 days

Solution:     Rajat can do the work in = 6 days

Jannat can do the work in = 12 days

Together they can do the work in = $\frac{1}{6}$+ $\frac{1}{12}$ = $\frac{3}{2}$ = $\frac{1}{4}$ = 4 days

Correct option: B

### Type 3: Calculate time/work when workers leave in between

Question 1. Three friends Anmol, Balbir and Chinu can do a work together in 12, 18, and 24 days respectively. After working 4 days Anmol and Chinu leaves the work. Find in how many days Balbir alone can complete the remaining work ?

Options:

A. 4 days

B. 5 days

C. 10 days

D. $\frac{18}{5}$ days

Solution:    (Anmol + Balbir + Chinu)’s one day work = $\frac{1}{12}$ +$\frac{1}{18}$+ $\frac{1}{24}$ = $\frac{13}{72}$

4’s day work = 4 × $\frac{13}{72}$ = $\frac{13}{18}$

Therefore, remaining work = 1 – $\frac{13}{18}$ =$\frac{5}{18}$

Now, time taken by Balbir to complete the work = $\frac{5}{18}$ × 18 = 5

Correct option: B

Question 2. Madhur can complete a part of task in 25 days. Her friend Divya can finish it in 20 days. They work together for 5 days and then Madhur left the work. In how many days will Divya finish the remaining work?

Options:

A. 24 days

B. 25 days

C. 20 days

D. 11 days

Solution:     Time taken by Madhur to finish the task = 25 days

Hence, Madhur’s one day work = $\frac{1}{25}$

Divya takes time to finish the work = 20 days

So, Divya’s one day’s work = $\frac{1}{20}$

Madhur + Divya’s 1 day’s work = $\frac{1}{25}$ + $\frac{1}{20}$ = $\frac{9}{100}$

Madhur + Divya’s 5 day’s work = 5 × $\frac{9}{100}$ = $\frac{9}{20}$

Therefore, remaining work (1 – $\frac{9}{20}$) = $\frac{11}{20}$

Now, $(\frac{11}{20})^{th}$ part of work is done by Divya in one day

Therefore, $\frac{11}{20}$ work will be done by Divya in 20 × $\frac{11}{20}$ = 11

Correct option: D

Question 3. Zubair can finish his assignment in 18 days. His brother Muneer can do the same assignment in 15 days. Muneer worked for 10 days and left the assignment. In how many days, Zubair alone can finish the remaining assignment?

Options:

A. 4 days

B. 5 days

C. 6 days

D. 8 days

Solution:     Muneer’s one day work on assignment = $\frac{1}{15}$ × 10 = $\frac{2}{3}$

Remaining work = 1 – $\frac{2}{3}$ = $\frac{1}{3}$

According to the question, A’s one day work = $\frac{1}{18}$

Therefore $\frac{1}{3}$ work is done by Zubair in $\frac{1}{3}$ × 18 = 6 days

Correct option: C

### Type 4: Share of salary based on work

Question 1. Raj and Ram undertook a work for Rs. 4000. Raj alone can do a part of work in 6 days. Ram alone can do a part of work in 8 days. Their friend Tony joined them and they completed the work in 3 days. What is the share of Tony ?

Options:

A. Rs. 500

B. Rs. 800

C. Rs. 300

D. Rs. 120

Solution:    Tony’s one day work = $\frac{1}{3}$ – ($\frac{1}{6}$ + $\frac{1}{8}$) = $\frac{1}{24}$

Their ratio of one day work = $\frac{1}{6}$: $\frac{1}{8}$: $\frac{1}{24}$

Tony worked for 3 days

Therefore, his share = 3 × $\frac{1}{24}$ × 4000 = 500.

Correct option:  A

Question 2. Kulfi can do a work in 10 days. Another girl joined and they complete the same work in 6 days. If they get Rs. 100 for the work, what is the share of another girl ?

Options:

A. Rs. 70

B. Rs. 60

C. Rs. 50

D. Rs. 10

Solution:    Kulfi can do the work in = 10 days

Both can do the work in = 6 days

Another girl can do the work = $\frac{1}{6}$$\frac{1}{10}$= $\frac{1}{15}$ = 15 days

Kulfi and another girl’s share = 15: 10 = 3: 2

Therefore, another girl’s share = $\frac{3}{5}$ × 100 = Rs. 60

Correct option:  B

Question 3. Arti, Ankit, and Nidhi contracted a work for Rs. 9999. Together, Arti and Ankit completed $\frac{7}{11}$ of the work. How much does Nidhi get ?

Options:

A. Rs. 3245

B. Rs. 3663

C. Rs. 6363

D. Rs. 3636

Solution:     Arti + Ankit did = $\frac{7}{11}$

Nidhi completed 1 – $\frac{7}{11}$ = $\frac{4}{11}$

Arti + Ankit’ share : Nidhi’s share = $\frac{7}{211}$: $\frac{4}{11}$

Nidhi’s share = $\frac{4}{11}$ × 9999 = 3636.

Correct option: D

Read Also –  Formulas to solve work and time questions