Time and Work Tricks :: Efficiency & Time Trick
Time and Work Tricks
Trick 1: Two People Working Together
Q1. A can do a work in 20 days, B in 30 days. How many days will A + B take together?
Formula / Trick: Days together = A×B / A+B
Soln: 20×30 / 20+30 = 600/50 = 12 days
Ans: 12 days
Trick 2: One Person Joins Later
Q2. A alone can do a work in 20 days. A + B together can do it in 15 days. Find B’s time.
Formula / Trick: B = AB / B-A
Soln: 15×20/20 -15 = 300/5 = 60 days
Ans: 60 days
Trick 3: Relative Work / Time Problem
Q3. A + B together = x days, A alone = x + 4 days, B alone = x + 16 days. Find x or A + B’s time.
Method: 1/A+1/B = 1/A+B
Substitute: 1/x+4+1/x+16=1/x
Solve:
LCM method: x(x+4)(x+16)
Solve quadratic → x = 8 days
Ans: x = 8 days
Trick 4: Three People Working Together
Q4. A = 3 days, B = 4 days, C = 6 days. Find time together.
Formula / Trick: Days together = A × B × C / AB + BC + CA
Soln: 3 × 4 × 6 / 3⋅4 + 4⋅6 + 6⋅3 = 72/12 + 24 + 18 = 72/54 = 1.33 days
Ans: 1.33 days (1 day 8 hours)
Short Tricks
1. Two persons together: A×B/A+B
2. One joins later: B = A×(A+B) / A+B−A
3. Three persons together: A×B×C / AB+BC+CA
4. Use efficiency: Work/day = 1/days; Total efficiency = sum; Days = 1/total efficiency
Q5. A alone can do a work in 6 days. A + B together can do it in 4 days. Find B’s time.
Soln: B = 6×4 / 6−4 = 24 / 2 = 12 days
Tricks : If A alone = x days, A + B = y days, Then, B = x y / x−y
Q6. A + B = 15 days, B + C = 10 days, A + C = 30 days. Find A + B + C = ? days
Trick: LCM + Efficiency Method
1st : LCM of 15, 10, 30 = 30,(Assume total work = 30 units)
2nd : Find efficiencies
- A + B → 30 ÷ 15 = 2 units/day
- B + C → 30 ÷ 10 = 3 units/day
- A + C → 30 ÷ 30 = 1 unit/day
3rd : Add efficiencies (A+B) + (B+C) + (A+C) = 2 + 3 + 1 = 6
But this equals : 2(A + B + C)
A + B + C = 6 ÷ 2 = 3 units/day
Find days: Days = 30/3 = 10 days
Ans: A+B+C=10 days
Exam Trick: LCM → find efficiencies → add → divide by 2 → divide total work
Q7. A = 20 days, B = 15 days, A + B + C = 6 days. Find C alone = ? days
Trick: LCM + EFFICIENCY METHOD
1st : Take LCM
LCM of 20, 15, 6 = 60 (Assume total work = 60 units)
2nd : Find efficiencies
- A → 60 ÷ 20 = 360 ÷ 20 = 3÷20=3 units/day
- B → 60 ÷ 15 = 460 ÷ 15 = 4÷15=4 units/day
- A + B + C → 60 ÷ 6 = 10 units/day
3rd : Find C’s efficiency: C = 10 - (3+4) = 3 units/day
4th : Find time taken by C : Time = 60 / 3 = 20 days
Ans: C = 20 days
Exam Trick: LCM → find efficiencies → subtract → divide total work
Q8. A = 20 days, B = 15 days, A + B + C = 6 days, Find A + C = ? days
Soln (LCM / Efficiency Trick)
1ST : Take LCM
LCM of 20, 15, 6 = 60 (total work)
2nd : Find efficiencies
- A → 60 ÷ 20 = 3 units/day
- B → 60 ÷ 15 = 4 60 ÷ 15 = 4 units/day
- A + B + C → 60 ÷ 6 = 10 units/day
3rd : Find C’s efficiency
C = 10 - (3 + 4) = 3 units/day
4th : Efficiency of A + C
A + C = 3 + 3 = 6 units/day
5th : Find days for A + C
Days = 60 / 6 = 10 days
Ans: A + C = 10 days
Efficiency & Time Trick
Basic Rqule
- Efficiency ∝ 1 / Time
- If Efficiency ratio = a : b then Time ratio = b : a
EXAM MEMORY LINE
Efficiency up → Time down
Efficiency × Time = Constant
Q9. If the efficiency of A : B = 2 : 3, then the time taken by A : B is :
Options: A) 2 : 3 B) 3 : 2 C) 5 : 6 D) 6 : 5
Ans: B) 3 : 2
Explanation: Efficiency ∝ 1 / Time. So, Time ratio = inverse of efficiency ratio = 3 : 2
Q10. A can do a work in 20 days. If the efficiency ratio of A : B = 6 : 5, then B will complete the work in:
Options: A) 15 days B) 18 days C) 24 days D) 30 days
Ans: 24 days
Explanation: Efficiency ∝ 1 / Time. Time ratio A : B = 5 : 6
So, B = 6/5 × 20 = 24 days
Q11. If A is 25% more efficient than B, then the ratio of time taken by A : B is:
Options: A) 4 : 5 B) 5 : 4 C) 3 : 4 D) 4 : 3
Ans: A) 4 : 5
Explanation: If A is 25% more efficient than B, then Efficiency ratio A : B = 125 : 100 = 5 : 4.
Q12. A takes 10 days and B takes 15 days to do a work. What is the efficiency ratio A : B ?
Options: A) 2 : 3 B) 3 : 2 C) 5 : 3 D) 3 : 5
Ans: 3 : 2
Explanation: Efficiency ∝ 1 / Time
A:B = 1/10:1/15 = 15:10 = 3:2
Q13. If A takes 12 days and B takes 18 days, then the ratio of time taken by A : B is:
Options: A) 2 : 3 B) 3 : 2 C) 4 : 3 D) 3 : 4
Ans: A) 2 : 3
Explanation: Time ratio = 12 : 18 = 2 : 3
Exam Rule
- Efficiency ratio = inverse of time ratio
- Efficiency × Time = constant