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Time and Work — REET Maths Notes

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This page covers REET maths' 'Time and Work' topic as per the syllabus — efficiency, one day's work, and how to solve pipes-and-cistern questions are explained through simple, verified examples. Time and Work appears in the syllabus for both REET Level 1 and Level 2 maths papers, so getting both the formulas and the underlying concept clear matters.

  • 0 questions in REET 2024 (syllabus-based notes)
  • Class 6–8 level
  • 8 min read
Verified 17 September 2026 · Source: BSER — REET आधिकारिक सिलेबस व 2024 प्रश्न-पत्र (मूल PDF; बोर्ड पोर्टल पर अब उपलब्ध नहीं)

How this topic is asked in REET

No direct question on 'Time and Work' was found in the REET 2024 paper records — meaning a question from this topic isn't guaranteed every year. But it's clearly included in the arithmetic section of the official BSER maths syllabus (Class 6–8 level), so skipping it in your preparation would be risky. All the notes, formulas and examples below are based purely on the syllabus wording and standard concepts — no reference is made to any imagined 'previous question'.

Core concept and formula

'Time and Work' is the branch of arithmetic that works out how long a person, machine or group takes to complete a task — alone, or together with others. The basic rule is: if a person A completes a task in 'a' days, then A's one day's work is taken as 1/a. The whole task is always treated as '1 unit', no matter what the actual work involves — that's the standard foundation for REET-level solutions.

If two people A and B complete a task in 'a' and 'b' days separately, then working together they will complete (1/a + 1/b) of the work in one day, and the time taken to finish the whole task together = ab/(a+b) days. The more people who join the work, the less time it takes — a direct example of inverse proportion, and the same principle underlies 'Men-Days' type questions.

Formulas worth knowing

A's one day's work
1/a (if A completes the task in 'a' days)
Time taken by A and B together
ab/(a+b) days
Men-Days rule
M₁D₁ = M₂D₂ (when the total quantity of work stays the same)
Filling rate of a pipe (inlet)
Fills the tank at a positive (+) rate
Emptying rate of a pipe (outlet)
Empties the tank at a negative (−) rate
Splitting work and wages
Always done in the ratio of efficiency, never in the ratio of days worked

Solving with the efficiency method

When a question says something like 'A is twice as efficient as B', the efficiency method is the fastest approach. Example: if A is twice as efficient as B, and together they complete a task in 12 days, then the efficiency ratio A:B = 2:1. Let B's one day's work = x, so A's = 2x. Together, 3x = 1/12, meaning x = 1/36. So A alone will finish the task in 18 days and B alone in 36 days. Check: 1/18 + 1/36 = 2/36 + 1/36 = 3/36 = 1/12 — which matches the given 12 days exactly.

Another example: A completes a task in 15 days and B completes the same task in 10 days. How many days will they take together? Solution: 1/15 + 1/10 = 2/30 + 3/30 = 5/30 = 1/6, meaning they'll complete the task together in 6 days. This same approach applies directly to any two-person question — add the rates, then take the reciprocal.

Worked examples: pipes-and-cistern and men-days

SituationSolution
Pipe A alone fills a tank in 6 hours, pipe B (an outlet) empties it in 9 hours — if both are open together, how long will the tank take to fill?1/6 − 1/9 = 3/18 − 2/18 = 1/18 ⇒ the tank fills in 18 hours
6 men complete a task in 10 days. How many men are needed to complete the same task in 5 days?M₁D₁ = M₂D₂ ⇒ 6×10 = M₂×5 ⇒ M₂ = 12 men
A, B and C together earn ₹1800 for a task; their efficiency ratio is 3:4:5 — how much does each get?Total parts = 3+4+5 = 12 ⇒ A = 450, B = 600, C = 750 (out of ₹1800)

Every value here has been solved and checked.

The alternate-days method

Sometimes REET-level questions have A and B working on alternate days — say A on day 1, B on day 2, and the pattern repeats. In such questions, the easiest approach is to work out how much of the task gets completed in one full cycle (as many days as there are people), and then find how many complete cycles are needed.

Example: A can complete a task in 10 days and B can complete the same task in 15 days. If they work on alternate days (A first, then B), how many days will the task take? Solution: in a 2-day cycle, the work done = 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6. Since 6 such cycles (12 days in total) complete 6×1/6 = 1 full task, the task will finish exactly on day 12 (B's day).

How to teach this to children

Activity

Have two or three students do the same task (such as folding 20 paper balloons) individually at different speeds, then note the actual time it takes when they work together — this makes the idea that 'working together reduces the time' clear through direct experience.

Teaching aid

Filling a bucket using two differently sized mugs or taps makes the pipes-and-cistern idea concrete, which makes writing the rate as a fraction feel more natural.

Common misconception

Students often make the mistake of adding the times directly instead of the rates (for example, 'A takes 12 days + B takes 18 days = 30 days together'), when the correct approach is to add the one-day work fractions (rates), not the number of days.

Assessment idea

Ask students 'what would happen to the time if the number of workers were doubled' and have them write a reasoned answer — this checks their understanding of inverse proportion.

A trick worth remembering

Always treat 'total work = 1 unit' and add or subtract rates (1/day) — never add or subtract the number of days directly. In pipes-and-cistern questions, always take the outlet (emptying pipe)'s rate as negative (−) — this is the single most common place mistakes happen.

Practice questions

Question 1

A can complete a work in 15 days and B in 10 days. In how many days will they complete it together?

  1. A5 दिन
  2. B12.5 दिन
  3. C25 दिन
  4. D6 दिन

Explanation

Rates of A and B: 1/15 + 1/10 = 2/30 + 3/30 = 5/30 = 1/6. So together they'll complete the task in 6 days.

Question 2

A is thrice as efficient as B and takes 20 days less than B to complete a work. In how many days can A alone finish the work?

  1. A30 दिन
  2. B6 दिन
  3. C10 दिन
  4. D15 दिन

Explanation

Let B = x days, so A = x/3 days (three times as efficient). Condition: x/3 = x − 20 ⇒ x − x/3 = 20 ⇒ 2x/3 = 20 ⇒ x = 30. So B = 30 days, A = 10 days (check: 30−10=20, the condition holds).

Question 3

12 men can complete a work in 8 days. How many men are needed to complete it in 6 days?

  1. A9
  2. B16
  3. C14
  4. D18

Explanation

M₁D₁ = M₂D₂ ⇒ 12×8 = M₂×6 ⇒ 96 = 6M₂ ⇒ M₂ = 16 men.

Question 4

A and B together can do a work in 12 days, B and C in 15 days, and A and C in 20 days. In how many days can A, B and C together complete the work?

  1. A10 दिन
  2. B15 दिन
  3. C5 दिन
  4. D20 दिन

Explanation

Adding all three given equations: 2(1/A+1/B+1/C) = 1/12+1/15+1/20 = 5/60+4/60+3/60 = 12/60 = 1/5. So 1/A+1/B+1/C = 1/10, meaning all three together complete the task in 10 days.

Question 5

Pipes A and B can fill a tank in 20 and 30 minutes respectively. Both are opened together, but to fill the tank in 18 minutes, after how long should pipe B be closed?

  1. A6 मिनट
  2. B12 मिनट
  3. C3 मिनट
  4. D9 मिनट

Explanation

A runs the full 18 minutes: 18/20 = 9/10 of the work. Remaining work = 1/10, done by B. B's rate is 1/30 per minute, so time = (1/10)÷(1/30) = 3 minutes. Check: 9/10 + 3/30(=1/10) = 1 complete task.

Question 6

A can finish a work in 18 days. He worked for 6 days and left. The remaining work was finished by B in 8 days. In how many days can B alone finish the whole work?

  1. A24 दिन
  2. B12 दिन
  3. C10 दिन
  4. D16 दिन

Explanation

A's 6 days of work = 6/18 = 1/3. Remaining work = 2/3, which B completed in 8 days, so B's rate = (2/3)/8 = 1/12. So B alone completes the task in 12 days.

Question 7

Which is the most suitable approach for a teacher to explain the concept of 'Time and Work' to Class 5 students?

  1. Aयह टॉपिक कक्षा 5 स्तर के लिए उपयुक्त नहीं, इसलिए न पढ़ाना
  2. Bकेवल सूत्र ab/(a+b) बोर्ड पर लिखकर रटवाना
  3. Cबिना उदाहरण के सीधे कठिन प्रश्न हल करवाना
  4. Dविद्यार्थियों से वास्तविक कक्षा-कार्य (जैसे बेंच साफ करना) अकेले व समूह में करवाकर समय की तुलना करवाना

Explanation

A concrete, experience-based activity lets children see for themselves that working together reduces the time, which makes the abstract formula feel meaningful afterward — this is far more effective than simple memorisation.

Question 8

A and B undertake to do a work for ₹720. A alone can do it in 6 days and B alone in 8 days. With the help of C, they finish it in 3 days. What is C's share?

  1. A₹90
  2. B₹180
  3. C₹120
  4. D₹60

Explanation

A's rate is 1/6, B's rate is 1/8; together all three work at rate 1/3. C's rate = 1/3 − (1/6+1/8) = 1/3 − 7/24 = 8/24−7/24 = 1/24. The rate ratio A:B:C = 4:3:1 (in multiples of 24). Total 8 parts = ₹720 ⇒ 1 part = ₹90, which is C's share.

Question 9

A can finish a work in 20 days. A and B together can finish it in 4 days. In how many days can B alone finish the work?

  1. A16 दिन
  2. B5 दिन
  3. C8 दिन
  4. D24 दिन

Explanation

1/A+1/B = 1/4 ⇒ 1/20+1/B = 1/4 ⇒ 1/B = 1/4−1/20 = 5/20−1/20 = 4/20 = 1/5. So B alone completes the task in 5 days.

Question 10

15 women can complete a work in 8 days. Assuming equal efficiency, in how many days will 12 women complete the same work?

  1. A6.4 दिन
  2. B9 दिन
  3. C10 दिन
  4. D20 दिन

Explanation

Total work = 15×8 = 120 woman-days. Time for 12 women = 120/12 = 10 days.

Frequently asked questions

How many questions come from 'Time and Work' in the REET exam?+

No direct question from this topic was found on record in REET 2024, but it is included in the official BSER maths syllabus, so it should still be treated as a required part of preparation for future exams.

What is the fastest way to solve Time and Work questions?+

The efficiency (rate) method is the fastest — write each person's one day's work as a fraction (1/day), add or subtract these, then take the reciprocal to find the total time.

What do inlet and outlet mean in pipes-and-cistern questions?+

An inlet pipe fills the tank, so its rate is taken as positive, while an outlet pipe empties the tank, so its rate is taken as negative — when both are open together, the rates are added.

What is the 'Men-Days' rule and when is it used?+

When the total quantity of work stays the same, the product of the number of men and the number of days stays constant (M₁D₁ = M₂D₂) — this is used when you need to find the new time taken after the number of workers changes.

How do you solve alternate-days work questions?+

First work out how much of the task gets completed in one full cycle (as many days as there are people), then check how many complete cycles finish the task — add the next person's day separately for any work still remaining.

Read next

Average — REET Notes

Previous topic: read about the concept and formulas of averages.

Time, Speed and Distance — REET Notes

Next topic: read about the concept and formulas of time, speed and distance.

REET Syllabus 2024

See the complete official REET Level 1 and Level 2 syllabus, subject-wise.

REET 2024 Solved Papers

Read the REET 2024 previous papers with answers and explanations.

Official Sources

  1. BSER — REET आधिकारिक सिलेबस व 2024 प्रश्न-पत्र (मूल PDF; बोर्ड पोर्टल पर अब उपलब्ध नहीं)

Change Log

  • 17 September 2026 — English page published — mirrors the fact-checked Hindi page, independently bilingual-accuracy checked