Page 3 – Quant (Time & Work)
Problem • Step-wise Solution • Tricks
Q1. A can do a work in 10 days, B in 15 days. Find together time.
Step 1: Take LCM of 10 and 15
LCM = 30 (Total work)
Step 2: Find efficiency
A = 30 ÷ 10 = 3 units/day
B = 30 ÷ 15 = 2 units/day
Step 3: Total work per day
3 + 2 = 5 units/day
Step 4: Time = Total work ÷ total efficiency
30 ÷ 5 = 6 days
Answer: 6 days
Trick: LCM → Efficiency → Add → Divide
Q2. A can do work in 12 days, B in 18 days. Find together time.
Step 1: LCM = 36
Step 2: Efficiency
A = 36 ÷ 12 = 3
B = 36 ÷ 18 = 2
Step 3: Total efficiency
3 + 2 = 5
Step 4: Time
36 ÷ 5 = 7.2 days
Answer: 7.2 days
Q3. A alone can do a work in 8 days. B alone can do same work in 8 days. Together?
Step 1: Same work rate
Step 2: Together work doubles
Step 3: Time becomes half
8 ÷ 2 = 4 days
Answer: 4 days
Trick: Same efficiency → time halves
Q4. A can do work in 20 days. What work in 1 day?
Step 1: Work per day = 1/20
Answer: 1/20 work
Trick: Work = 1 / Days
Q5. A does 1/10 work in 1 day. How many days to complete work?
Step 1: In 1 day → 1/10 work
Step 2: Total work = 1
Step 3: Days = 10
Answer: 10 days
Trick: Reverse logic
Important Formulas
Work = Efficiency × Time
Efficiency = Work / Time
Time = Work / Efficiency
Shortcut Tips
- Use LCM for faster solving
- Add efficiencies, not time
- Same workers → time halves
Final Tip
Think in terms of work units, not days
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