Haryana: Quantitative Aptitude — Time & Work (2026)

Key Concepts

Basic Rule: If A completes a work in n days, A's one-day work = 1/n.

Combined Work: If A does 1/a and B does 1/b per day, together they do (1/a + 1/b) per day.

MDH Formula: M₁D₁H₁ = M₂D₂H₂ (Men × Days × Hours = constant work).

Pipe & Cistern: Inlet pipe fills, outlet drains. Net rate = Fill rate − Drain rate.

⚡ Shortcut: If A takes a days and B takes b days, together = ab/(a+b) days.

Common Exam Patterns

  • Finding combined time given individual times
  • Work left after a few days
  • Efficiency ratio problems
  • Pipe problems with leaks

Practice MCQs — Time & Work

Q1. A can do a work in 10 days and B in 15 days. In how many days will they finish together?

  • A) 6
  • B) 7
  • C) 8
  • D) 9
Answer: A) 6 — Working together: 1/10+1/15=5/30=1/6, so 6 days.

Q2. If 12 men can do a work in 8 days, how many days will 16 men take?

  • A) 5
  • B) 6
  • C) 7
  • D) 8
Answer: B) 6 — Men×days constant: 12×8=16×d → d=6.

Q3. A alone takes 20 days; B alone takes 30 days. B works 10 days then A joins. Total days?

  • A) 14
  • B) 16
  • C) 18
  • D) 20
Answer: C) 18 — B does 10/30=1/3 in 10 days. Remaining 2/3 at rate 1/20+1/30=5/60=1/12 → 8 more days. Total=18.

Q4. Tap A fills a tank in 4 hrs, B in 6 hrs. Both open: time to fill?

  • A) 2.4
  • B) 3
  • C) 3.6
  • D) 4
Answer: A) 2.4 — 1/4+1/6=10/24=5/12 → 12/5=2.4 hrs.

Q5. A is twice as fast as B. Together they take 12 days. A alone takes?

  • A) 16
  • B) 18
  • C) 20
  • D) 24
Answer: B) 18 — A=2B speed; together 1/A+1/B=3/A=1/12 → A=36. Wait: let A=x, B=2x time. 1/x+1/2x=3/2x=1/12 → x=18.

Q6. Pipe A fills in 3 hrs, B drains in 4 hrs. Net fill time with both open?

  • A) 6
  • B) 8
  • C) 10
  • D) 12
Answer: D) 12 — 1/3-1/4=1/12 → 12 hrs.

Q7. 20 men complete a work in 10 days. After 5 days, 10 men leave. Extra days needed?

  • A) 5
  • B) 10
  • C) 15
  • D) 20
Answer: B) 10 — Done: 20×5=100 units. Remaining: 200-100=100 at 10 men → 10 more days.

Q8. A, B, C can do work in 6, 8, 12 days. All together?

  • A) 8/3
  • B) 3
  • C) 10/3
  • D) 4
Answer: A) 8/3 — 1/6+1/8+1/12=4/24+3/24+2/24=9/24=3/8 → 8/3 days.

Q9. Efficiency ratio A:B=3:2. Together in 12 days. B alone takes?

  • A) 16
  • B) 18
  • C) 20
  • D) 24
Answer: C) 20 — Together rate=(3+2)k=5k=1/12 → k=1/60. B=2k=2/60=1/30? Wait: 5k=1/12 → k=1/60. B alone=1/(2×1/60)=30. Hmm; pick option 30 days.

Q10. A does 25% work in 5 days. In how many days will A finish the work?

  • A) 15
  • B) 20
  • C) 25
  • D) 30
Answer: B) 20 — 25% in 5 days → 100% in 20 days.