# How to solve quickly

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.

## Type1: 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 = ½ (1/12 + 1/15 + 1/20)

Rohan + Mohan + Soham one day work =1/10

Now, Rohan’s one day work = 1/10 – 1/15 = 1/30
Therefore, Rohan alone will paint the wall in 30 days.

### 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 1/2

B. 13 days

C.16 days

D. 4 2/3 days

#### Solution:

Mamta can finish part of assignment in one day = 1/8

Sunil can finish part of assignment in one day = 1/16

Mamta + Sunil together finish part of assignment in one day = 1/8 + 1/16 = 3/16

Therefore, together they will take 16/3 days = 5 (1/3)days

### 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 = 1/24 – 1/60 = 1/40

Therefore, she will take 40 days

## Type 2: Calculate time/work when efficiency is given in percentage

### Question 1.

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

Options

A.40 days

B. 30 days

C. 20days

D. 35 days

#### Solution

time required to complete the job together is given by =

T = m * D/ (m2 – 1)

T = 2 * 30/ (22-1)

T =60/3

T= 20 days

### 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. 10days

C. 25days

D. 15 days

#### Solution:

1student= 2 professionals (as given in question, efficiency of each student is twice that of a professionals)
6 students = 12 professionals
As given
(students + 3 professionals* 8 * 12 = 12 professionals * 6 * D
15 professionals * 8 * 12 = 12 girls * 6 * D
D = 20

### 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. 2.22 days

B. 3.33days

C. 4.44 days

D. 1.25days

#### Solution:

Efficiency of Rajat is twice of Jannat

This means Rajat efficiency to complete the assignment = 20%

Jannat’s efficiency to complete the assignment = 10%

Together their efficiency = 30%

To complete the work they will take 100/30 = 3.33 days

## 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. 18/5 days

#### Solution:

(Anmol + Balbir + Chinu)’s one day work = 1/12 + 1/18+ 1/24 = 13/72

4’s day work = 4 * 13/72 = 13/18

Therefore, remaining work = 1 – 13/18 = 5/18

Now, time taken by Balbir to complete the work = 5/18 * 18 = 5

### 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. 11days

#### Solution:

hence, Madhur’s one day work = 1/25
Divya takes time to finish the work = 20 days
So, Divya’s one day’s work = 1/20
Madhur + Divya’s 1 day’s work = 1/25 + 1/20 = 9/100
Madhur + Divya’s 5 day’s work = 5 * 9/ 100 = 9/20
Therefore, remaining work (1  9/20) = 11/20
Now, 11/20th part of work is done by Divya in one day
Therefore, 11/20 work will be done by Divya in 20 * 11/20  = 11

### 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. 6days

D. 8days

#### Solution:

Muneer’s one day work on assignment = 1/15 * 10 = 2/3

Remaining work = 1 – 2/3 = 1/3

According to the question, A’s one day work = 1/18

Therefore 1/3 work is done by Zubair in 1/3 * 18 = 6 days

## 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. Rs500

B. Rs. 800

C. Rs.300

D. Rs.120

#### Solution:

Tony’s one day work = 1/3 – (1/6 + 1/8) = 1/24

Their ratio of one day work = 1/6: 1/8: 1/24

Tony worked for 3 days

Therefore, his share = 3 * 1/ 24 * 4000 = 500

### 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. Rs70

B. Rs. 60

C. Rs.50

D. Rs.10

#### Solution:

Another girl can do the work = 10 * 6/10 – 6 = 15 days

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

Therefore, another girl’s share = 100/5 * 3 = Rs. 60

### Question 3.

Arti, Ankit, and Nidhi contracted a work for Rs. 9999. Together, Arti and Ankit completed 7/11 of the work. How much does Nidhi get?

Options

A. Rs3245

B. Rs. 3663

C. Rs.6363

D. Rs.3636

#### Solution:

Arti + Ankit did = 7/11

Nidhi completed 1 – 7/11 = 4/11

Arti + Ankit’ share : Nidhi’s share = 7/11: 4/11

Nidhi’s share = 9999/11 * 4 = 3636