Time & Work Set 1
Shortcut Points
1. More days = Less efficiency
Efficiency ∝ 1/days
2. LCM Method (Fastest)
· Take LCM of days to assume total work
· Convert into work units per day
· Divide remaining units by daily units to get time
3. Fraction Method (Classic)
Together work = 1/x + 1/y
4. Portion Completion Rule
Completed work = days worked × 1-day work
5. Remaining Work
1 – completed or Total units − done units
6. Leaving / Joining Rule
· When someone leaves → remaining work done by rest
· When someone joins → speed increases
7. Partial Days
If work left is not whole number, use fraction directly.
Examples:
Q. Julie can cover 140 meters in 18 seconds. At the same speed, how much distance will she cover in 1 hour ?
Options: (a) 25.2 km (b) 31.5 km (c) 28 km (d) 29.4 km
Soln
Calculate Speed
Speed = Distance/Time = 140/18 m/s
Convert m/s to km/h
1 m/s = 18/5 km/h
140/18 × 18/5
Cancel 18:140 / 5 = 28 km/h
Ans = 28 km/h
Final Distance in 1 Hour
Since speed = 28 km/h, Distance in 1 hour = 28 km
Ans: (c) 28 km
Shortcut
Speed (km/h) = Distance in m / Time in sec × 18/5
=140/18 × 18/5 = 28km
Simple Level
1. A alone can finish a work in 10 days. B alone in 20 days. Together ?
Trick: LCM = 20
A’s 1 - day work = 2
B’s 1 - day work = 1
Total = 3 units/day
Time = 20/3 = 6 2/3 days
Ans: 6 days 16 hours
2. A can do a job in 6 days, B can do in 3 days. Together ?
Trick: LCM = 6
A = 1 unit/day
B = 2 units/day
Total = 3 units/day
6/3 = 2 days
Ans: 2 days
3. A completes work in 15 days, B in 5 days. Together?
Trick: LCM = 15
A = 1 unit/day
B = 3 unit/day
Total = 4 units/day
15/4 = 3.75 = 3 ¾
Ans: 3 days 18 hours
Trick : Together work = LCM / (sum of 1-day work)
Medium Level: Trick : Helping work → subtract work completed → rest handled by helper.
4. A alone = 12 days, B alone = 8 days. If they work together for 3 days, remaining work ?
1-day work:
· A = 1/12
· B = 1/8
= 2+3/24 = 5/24
Work in 3 days: 3×5/24=15/24=5/8
Remaining:1- 5/8 = 3/8
Ans: 3/8 work left
5. A = 18 days, B = 9 days. If B works only 3 days then A alone finishes rest. Total time?
1-day work:
· A = 1/18
· B = 1/9 = 2/18
Work by B in 3 days: 3×2/18 = 6/18 = 1/3
Left: 1-1/3 = 2/3
Now A finishes: 2/3 divide 1/18 = 2/3×18 =12
Total: 3+12=15 days
Ans: 15 days
6. A = 20 days, B = 30 days. C helps only 5 days. Total 10 days work done. C’s 1-day work ?
A + B = 1/20 + 1/30 = 5/60 = 1/12
10 days without C: 10/12 = 5/6
Work done by C in 5 days = remaining
` 1 − 5/6 = 1/6
C’s 1- day work: 1/6 divide 5 = 1/6*1/5 = 1/30
Ans: C = 30 days alone
TOUGH
7. A = 12 days, B = 15 days, C = 20 days. All start, C leaves after 3 days. Total?
LCM = 60
· A = 5 units/day
· B = 4 units/day
· C = 3 units/day
Total = 12 units/day
3 days work: 12×3=36
Left: 60- 36 = 24
Now A + B → 5 + 4 = 9 units/day
Time: 24/9 = 2 6/9 = 2 2/3
Ans: 5 days 16 hours
8. A = 8 days, B = 24 days. A works alone 4 days then B joins. Total time ?
LCM = 24
A = 3
B = 1
Work by A in 4 days: 3×4=123
Left: 24 – 12 = 12
A + B: 3+1=4
Time:12/4 = 3 days
Total: 4+3=7 days
Ans: 7 days
9. A = 10 days, B = 15 days, C = 30 days. B leaves after half work. Total ?
LCM = 30
- A = 3 units/day
- B = 2 units/day
- C = 1 units/day
Total = 6 units/day
Half work done: 30/2 = 15units
Time for half:15/6 = 2.5 days
Now B leaves, A + C: 3+1=4
Remaining:15units
Time:15/4=3.75
Total: 2.5+3.75 = 6.25 days
Ans: 6.25 days
Trick 1: Leaving / Joining Trick (Fastest Method)
When one worker leaves after t days: Work done = t×(Total 1-day work)
Leftover work: Remaining =1−completed
Then remaining workers finish.
Used for:
· “C leaves after 3 days”
· “B joins after 5 days”
Trick 2: Efficiency Shortcut (Fast Ratio Method)
If:
A:B = efficiency ratio
Time ratio = 1/efficiency
Trick 3: Half / Part work shortcut
If half work done by ABC, rest by AB only:
Half work time = ½ divided combined rate
Shortcut Points
1. More days = Less efficiency
Efficiency ∝ 1/days
2. LCM Method (Fastest)
- Take LCM of days to assume total work
- Convert into work units per day
- Divide remaining units by daily units to get time
3. Fraction Method (Classic)
Together work = 1/x + 1/y
4. Portion Completion Rule
Completed work = days worked × 1-day work
5. Remaining Work
1 – completed or Total units − done units
6. Leaving / Joining Rule
- When someone leaves → remaining work done by rest
- When someone joins → speed increases
7. Partial Days
If work left is not whole number, use fraction directly.