How To Solve Time and Work Problems Quickly

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 = 7 : 4

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

Correct option: D