Time and Work

Work rate, efficiency, combined work

107 practice questionsPage updated 27 Mar 2026Review metadata pendingPractice questions

Time and Work problems deal with the relationship between the time taken to complete a task and the efficiency or rate at which workers operate. These problems typically involve calculating how long individuals or groups take to finish jobs, determining work rates, and solving scenarios involving combined efforts, efficiency variations, and partial work completion.

Key formulas and rules

Work Rate = 1 / Time (work done per unit time)

Time = Work / Rate

If A can do a work in 'n' days, A's 1 day work = 1/n

If A's 1 day work = 1/n, A can finish the work in 'n' days

Combined rate of A and B = (1/a + 1/b) where a, b are individual times

Time taken by A and B together = (a x b) / (a + b)

If A is 'x' times more efficient than B: If B takes 'n' days, A takes n/x days

Man-Days = Number of men x Number of days (constant for same work)

M x D = M x D (for same work with different men and days)

M x D x H = M x D x H (including hours per day)

Work done = (Days worked) / (Total days to complete)

Remaining work = 1 - Work already done

Key concepts

Basic Work Rate Concept

The fundamental principle is that if a person can complete a work in 'n' days, their daily work rate is 1/n of the total work. For example, if A completes work in 10 days, A does 1/10 of the work each day. This fraction represents the portion of work completed per day and forms the basis for all time and work calculations.

Combined Work (Working Together)

Worked examples

Example 1

A can complete a work in 15 days and B can complete the same work in 20 days. If they work together, how many days will they take to complete the work?

Solution

Step 1: Find individual work rates.
A's 1 day work = 1/15
B's 1 day work = 1/20

Step 2: Calculate combined work rate.
(A + B)'s 1 day work = 1/15 + 1/20
= 4/60 + 3/60
= 7/60

Step 3: Find time taken together.
Time = 1 / (7/60) = 60/7 days
= 8(4/7) days

Answer: 60/7 days or approximately 8.57 days

Example 2

A and B together can complete a work in 12 days. B and C together can complete it in 15 days. C and A together can complete it in 20 days. How many days will A, B, and C take to complete the work together?

Solution

Step 1: Set up equations from given information.
(A + B)'s 1 day work = 1/12 ... (1)
(B + C)'s 1 day work = 1/15 ... (2)
(C + A)'s 1 day work = 1/20 ... (3)

Step 2: Add all three equations.
2(A + B + C)'s 1 day work = 1/12 + 1/15 + 1/20
= 5/60 + 4/60 + 3/60
= 12/60
= 1/5

Step 3: Find combined rate of all three.
(A + B + C)'s 1 day work = (1/5) / 2 = 1/10

Step 4: Calculate time taken.
Time = 1 / (1/10) = 10 days

Answer: 10 days

Example 3

A is twice as efficient as B. Together they complete a work in 18 days. How many days will A alone take to complete the work?

Solution

Step 1: Establish efficiency relationship.
If B's 1 day work = 1/x, then A's 1 day work = 2/x (since A is twice as efficient)

Step 2: Use combined work information.
(A + B)'s 1 day work = 1/18
2/x + 1/x = 1/18
3/x = 1/18
x = 54

Step 3: Find A's time.
B takes 54 days
A takes 54/2 = 27 days (since twice as efficient)

Verification: 1/27 + 1/54 = 2/54 + 1/54 = 3/54 = 1/18

Answer: 27 days

Example 4

20 men can complete a work in 30 days. After working for 10 days, 5 more men join. In how many more days will the work be completed?

Solution

Step 1: Calculate total work in man-days.
Total work = 20 men x 30 days = 600 man-days

Step 2: Calculate work done in first 10 days.
Work done = 20 men x 10 days = 200 man-days

Step 3: Find remaining work.
Remaining work = 600 - 200 = 400 man-days

Step 4: Calculate new team capacity.
New team = 20 + 5 = 25 men

Step 5: Find days needed to complete remaining work.
Days = 400 man-days / 25 men = 16 days

Answer: 16 more days

Time and Work

Key formulas and rules

Key concepts

Basic Work Rate Concept

Combined Work (Working Together)

Efficiency and Comparison

Man-Days (Men and Work)

Partial Work and Remaining Work

Alternating Work (A and B Working on Alternate Days)

Worked examples

Example 1

Example 2

Example 3

Example 4

Representative solved questions

Question 1

Question 2

Question 3

Common mistakes and useful habits

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Key formulas and rules

Key concepts

Basic Work Rate Concept

Combined Work (Working Together)

Efficiency and Comparison

Man-Days (Men and Work)

Partial Work and Remaining Work

Alternating Work (A and B Working on Alternate Days)

Worked examples

Example 1

Example 2

Example 3

Example 4

Representative solved questions

Question 1

Question 2

Question 3

Common mistakes and useful habits

Ready to test your understanding?

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