Math 3- Shortcut tricks and smart strategies to solve Time and Work problems faster, especially useful for CDS, SSC, UPSC, and other competitive exams

Math 3- Shortcut tricks and smart strategies to solve Time and Work problems faster-especially useful for CDS, SSC, UPSC, and other competitive exams:

Time and Work Shortcut Tricks

🔹 1. Assume Total Work = LCM of Days

Instead of assuming total work as 1 unit, take the LCM of the number of days to simplify calculations.

Example:
A can do a job in 10 days, B in 15 days.
LCM of 10 and 15 = 30 units
A’s efficiency = 30/10 = 3 units/day
B’s efficiency = 30/15 = 2 units/day
Together = 5 units/day → Time = 30/5 = 6 days

✅ Why it works: You avoid fractions and get clean unit-based answers.

🔹 2. Use the Inverse Formula for “Together Work”

If A takes x days, B takes y days:
Time together = (x × y) / (x + y)

Example:
A = 10 days, B = 15 days
Time together = (10 × 15)/(10 + 15) = 150/25 = 6 days

🔹 3. Efficiency Ratio = Inverse of Time

If A takes 10 days, B takes 5 days:
Efficiency ratio = B:A = 10:5 → Reverse = 1/10 : 1/5 = 1:2
So B is twice as efficient as A.

🔹 4. Work Done = Efficiency × Time

If A’s efficiency is 5 units/day and works for 4 days:
Work done = 5 × 4 = 20 units

🔹 5. Pipes and Cisterns = Time and Work with Signs

Treat inlet as positive, outlet as negative.

Example:
Pipe A fills in 6 hrs (+1/6), Pipe B empties in 12 hrs (–1/12)
Net rate = 1/6 – 1/12 = 1/12
Time to fill = 1 ÷ (1/12) = 12 hrs

🔹 6. Alternate Days Work

If A and B work on alternate days, calculate total work done in 2-day cycles.

Example:
A = 5 units/day, B = 3 units/day
In 2 days = 5 + 3 = 8 units
Total work = 40 units → 5 cycles = 10 days

🔹 7. Work and Wages Distribution

Wages ∝ Efficiency ∝ Work done

Example:
A = 10 days, B = 5 days → Efficiency = 1/10 : 1/5 = 1 : 2
Total wage = ₹900 → A gets ₹300, B gets ₹600

🔹 8. If Work is Partially Done

Use fractions to track progress.

Example:
A does 1/3 of work in 5 days → Full work = 5 × 3 = 15 days

🔹 9. Reverse Work Problems

If someone finishes work in x days, and someone else undoes it in y days, use net rate.

Example:
A fills in 4 hrs (+1/4), B empties in 6 hrs (–1/6)
Net rate = 1/4 – 1/6 = (3 – 2)/12 = 1/12
Time = 12 hrs

🔹 10. Use Smart Approximations

If options are close, estimate using decimals.

Example:
A = 7 days, B = 14 days → Together = (7×14)/(7+14) = 98/21 ≈ 4.67 days

Practice more questions with shortcut tricks . Maths is more about practices.