Q1): A can complete a work in 24 days and B in 36 days. They work together, but A leaves after 6 days. Total time to finish the work is:
A) 24 days
B) 25 days
C) 27 days
D) 30 days
Answer: C) 27 days
Explanation:
- Step 1: A’s 1-day work = 1/24, B’s 1-day work = 1/36
- Step 2: Together 1-day work = 1/24 + 1/36 = 5/72
- Step 3: Work done in 6 days = 6 × 5/72 = 5/12
- Step 4: Remaining work = 1 − 5/12 = 7/12
- Step 5: B alone time = (7/12) ÷ (1/36) = 21 days
- Final: Total time = 6 + 21 = 27 days → option C
Q2): A and B together can complete a work in 12 days. They work together for 5 days, then B leaves. A alone finishes the remaining work. Total time is:
A) 15 2/3 days
B) 16 2/3 days
C) 17 2/3 days
D) 18 2/3 days
Answer: B) 16 2/3 days
Explanation:
- Step 1: (A+B) 1-day work = 1/12
- Step 2: Work done in 5 days = 5/12
- Step 3: Remaining work = 1 − 5/12 = 7/12
- Step 4: Given A alone can do it in 20 days ⇒ A’s rate = 1/20
- Step 5: A’s time for remaining = (7/12) ÷ (1/20) = 35/3 = 11 2/3 days
- Final: Total time = 5 + 11 2/3 = 16 2/3 days → option B
Q3): A can do a work in 18 days and B in 24 days. They start together. After 6 days, A’s efficiency decreases by 25%. Total time to finish the work is:
A) 10 days
B) 11 days
C) 12 days
D) 13 days
Answer: B) 11 days
Explanation:
- Step 1: A’s rate = 1/18, B’s rate = 1/24
- Step 2: Initial together rate = 1/18 + 1/24 = 7/72
- Step 3: Work done in 6 days = 6 × 7/72 = 7/12
- Step 4: Remaining work = 1 − 7/12 = 5/12
- Step 5: A becomes 25% less efficient ⇒ new A rate = 75% of (1/18) = 1/24
- Step 6: New together rate = 1/24 + 1/24 = 1/12
- Final: Time for remaining = (5/12) ÷ (1/12) = 5 days, so total = 6 + 5 = 11 → option B
Q4): Pipe A fills a tank in 8 hours and pipe B in 12 hours. Both start together. After 2 hours, an outlet opens that empties the full tank in 24 hours. Total time to fill the tank is:
A) 5 1/3 hours
B) 5 1/2 hours
C) 5 2/3 hours
D) 6 hours
Answer: B) 5 1/2 hours
Explanation:
- Step 1: Fill rate (A+B) = 1/8 + 1/12 = 5/24 tank/hr
- Step 2: Filled in first 2 hours = 2 × 5/24 = 5/12
- Step 3: Remaining = 1 − 5/12 = 7/12
- Step 4: After outlet opens, net rate = 5/24 − 1/24 = 1/6
- Step 5: Time for remaining = (7/12) ÷ (1/6) = 7/2 = 3 1/2 hours
- Final: Total time = 2 + 3 1/2 = 5 1/2 hours → option B
Q5): 24 men working 6 hours/day can finish a work in 15 days. After 10 days, 6 men leave and the remaining men work 8 hours/day. Total days to finish the work are:
A) 14 days
B) 15 days
C) 16 days
D) 17 days
Answer: B) 15 days
Explanation:
- Step 1: Total work = 24 × 6 × 15 = 2160 man-hours
- Step 2: Work done in 10 days = 24 × 6 × 10 = 1440 man-hours
- Step 3: Remaining work = 2160 − 1440 = 720 man-hours
- Step 4: New daily work = (24−6) × 8 = 18 × 8 = 144 man-hours/day
- Step 5: Days for remaining = 720 ÷ 144 = 5 days
- Final: Total days = 10 + 5 = 15 days → option B
Q6): A can do a work in 12 days and B in 18 days. They work together for 6 days, then A leaves. B finishes the remaining work. If total wages are ₹8400, B’s share is:
A) ₹3600
B) ₹4000
C) ₹4200
D) ₹4800
Answer: C) ₹4200
Explanation:
- Step 1: A’s rate = 1/12, B’s rate = 1/18
- Step 2: B’s work in 6 days (while together) = 6 × 1/18 = 1/3
- Step 3: Remaining work after 6 days together = 1 − 6×(1/12+1/18) = 1 − 6×(5/36) = 1 − 5/6 = 1/6
- Step 4: B alone completes remaining 1/6, so B’s total work = 1/3 + 1/6 = 1/2
- Step 5: B’s wages = (1/2) × 8400 = 4200
- Final: So option C is correct
Q7): A+B can finish a work in 10 days, B+C in 12 days, and A+C in 15 days. A alone can finish the work in:
A) 20 days
B) 24 days
C) 30 days
D) 40 days
Answer: B) 24 days
Explanation:
- Step 1: Rates: (A+B)=1/10, (B+C)=1/12, (A+C)=1/15
- Step 2: (A+B) + (A+C) = 1/10 + 1/15 = 1/6
- Step 3: This equals 2A + (B+C)
- Step 4: So 2A = 1/6 − 1/12 = 1/12 ⇒ A’s rate = 1/24
- Final: A alone time = 24 days → option B
Q8): A can complete a work in 10 days, B in 15 days. They work on alternate days starting with A, but A works only 80% of a day whenever it is A’s turn. The work will finish in:
A) 13 2/5 days
B) 13 3/5 days
C) 14 1/5 days
D) 14 3/5 days
Answer: B) 13 3/5 days
Explanation:
- Step 1: A’s full-day rate = 1/10, effective rate = 80% of 1/10 = 2/25
- Step 2: B’s rate = 1/15
- Step 3: Work in 2 days (A then B) = 2/25 + 1/15 = 11/75
- Step 4: In 12 days (6 cycles), work = 6 × 11/75 = 66/75 = 22/25
- Step 5: Remaining = 1 − 22/25 = 3/25
- Step 6: Next is A: after 1 A-day, remaining = 3/25 − 2/25 = 1/25
- Final: B finishes 1/25 in time = (1/25) ÷ (1/15) = 3/5 day, total = 13 + 3/5 → option B
Q9): 6 men and 8 boys can complete a work in 12 days. 10 men and 4 boys can complete it in 8 days. Time taken by 8 men and 6 boys is:
A) 9 1/5 days
B) 9 2/5 days
C) 9 3/5 days
D) 10 days
Answer: C) 9 3/5 days
Explanation:
- Step 1: Let 1 man’s rate = m, 1 boy’s rate = b
- Step 2: 6m + 8b = 1/12 and 10m + 4b = 1/8
- Step 3: Multiply second by 2: 20m + 8b = 1/4
- Step 4: Subtract first: (20m−6m) = 1/4 − 1/12 = 1/6 ⇒ 14m = 1/6 ⇒ m = 1/84
- Step 5: Put m in 10m + 4b = 1/8 ⇒ 10/84 + 4b = 1/8 ⇒ 4b = 1/168 ⇒ b = 1/672
- Step 6: Rate of 8 men and 6 boys = 8/84 + 6/672 = 2/21 + 1/112 = 5/48
- Final: Time = 1 ÷ (5/48) = 48/5 = 9 3/5 days → option C
Q10): Pipe A fills a tank in 9 hours, pipe B fills it in 12 hours, and a leak empties it in 18 hours. All are opened together, but after 3 hours pipe B is closed. Total time to fill the tank is:
A) 12 1/2 hours
B) 13 hours
C) 13 1/2 hours
D) 14 hours
Answer: C) 13 1/2 hours
Explanation:
- Step 1: Initial net rate = 1/9 + 1/12 − 1/18 = 5/36 tank/hr
- Step 2: Filled in first 3 hours = 3 × 5/36 = 5/12
- Step 3: Remaining = 1 − 5/12 = 7/12
- Step 4: After closing B, net rate = 1/9 − 1/18 = 1/18
- Step 5: Time for remaining = (7/12) ÷ (1/18) = 21/2 = 10 1/2 hours
- Final: Total time = 3 + 10 1/2 = 13 1/2 hours → option C
Q11): A can do a work in 16 days and B in 24 days. They work together, but after completing half the work, B’s efficiency becomes double. Total time is:
A) 8 6/35 days
B) 8 8/35 days
C) 8 10/35 days
D) 9 days
Answer: B) 8 8/35 days
Explanation:
- Step 1: A’s rate = 1/16, B’s rate = 1/24
- Step 2: Initial together rate = 1/16 + 1/24 = 5/48
- Step 3: Time for first half = (1/2) ÷ (5/48) = 24/5 = 4 4/5 days
- Step 4: New B rate = 2 × (1/24) = 1/12
- Step 5: New together rate = 1/16 + 1/12 = 7/48
- Step 6: Time for remaining half = (1/2) ÷ (7/48) = 24/7 = 3 3/7 days
- Final: Total time = 24/5 + 24/7 = 288/35 = 8 8/35 days → option B
Q12): A, B, and C can complete a work in 20, 30, and 60 days respectively. They work together for 5 days, then A leaves. After 5 more days, B also leaves. C finishes the remaining work alone. Total time is:
A) 20 days
B) 22 days
C) 25 days
D) 30 days
Answer: C) 25 days
Explanation:
- Step 1: Rates: A=1/20, B=1/30, C=1/60
- Step 2: Together rate (A+B+C) = 1/10
- Step 3: Work in first 5 days = 5 × 1/10 = 1/2
- Step 4: Remaining = 1 − 1/2 = 1/2
- Step 5: Rate of (B+C) = 1/30 + 1/60 = 1/20
- Step 6: Work in next 5 days = 5 × 1/20 = 1/4, remaining = 1/2 − 1/4 = 1/4
- Final: C alone time = (1/4) ÷ (1/60) = 15 days, total = 5+5+15 = 25 → option C
Q13): A can do a work in 12 days, B in 18 days, and C in 24 days. They all work together for 4 days. Then B leaves; A works with C for 1 day. Then A also leaves and C finishes the work. If total wages are ₹9900, B’s share is:
A) ₹2000
B) ₹2200
C) ₹2400
D) ₹2750
Answer: B) ₹2200
Explanation:
- Step 1: B works only during first 4 days
- Step 2: B’s 1-day work = 1/18
- Step 3: B’s total work = 4 × 1/18 = 2/9
- Step 4: Wages are divided in the ratio of work done
- Step 5: B’s share = (2/9) × 9900 = 2200
- Final: So option B is correct
Q14): A is 20% less efficient than B, and C is 25% more efficient than B. If A can complete a work in 25 days, then A, B, and C together will complete it in:
A) 8 1/2 days
B) 8 13/14 days
C) 9 1/2 days
D) 10 days
Answer: B) 8 13/14 days
Explanation:
- Step 1: A is 20% less efficient than B ⇒ A:B efficiency = 4:5
- Step 2: C is 25% more efficient than B ⇒ C:B efficiency = 5:4
- Step 3: So efficiency ratio A:B:C = 4:5:5
- Step 4: A’s time = 25 days ⇒ A’s rate = 1/25 corresponds to 4 parts
- Step 5: Total parts = 4+5+5 = 14 ⇒ total rate = (14/4)×(1/25) = 14/100 = 7/50
- Final: Time = 1 ÷ (7/50) = 50/7 = 7 1/7? wait, convert correctly: 100/14 = 50/7 = 7 1/7?
- Final: Using direct fraction from rates: A=1/25, B=5/4×1/25=1/20, C=5/4×B=1/16; sum = 1/25+1/20+1/16 = 14/125 ⇒ time = 125/14 = 8 13/14 → option B
Q15): A can do a work in 12 days, B in 18 days, and C in 24 days. They work together for 3 days. Then A leaves and B+C work for 2 days. Then only C works and finishes the remaining work. Total time is:
A) 10 1/3 days
B) 11 1/3 days
C) 12 1/3 days
D) 13 1/3 days
Answer: B) 11 1/3 days
Explanation:
- Step 1: Rates: A=1/12, B=1/18, C=1/24
- Step 2: Together rate (A+B+C) = 13/72
- Step 3: Work in first 3 days = 3 × 13/72 = 13/24
- Step 4: Remaining = 1 − 13/24 = 11/24
- Step 5: Rate of (B+C) = 1/18 + 1/24 = 7/72
- Step 6: Work in next 2 days = 2 × 7/72 = 7/36
- Step 7: Remaining = 11/24 − 7/36 = 19/72
- Final: C alone time = (19/72) ÷ (1/24) = 19/3 = 6 1/3; total = 3+2+6 1/3 = 11 1/3 → option B
Q16): A tank is already 1/4 full. Pipe A fills the tank in 12 hours, pipe B fills it in 18 hours, and a leak empties it in 24 hours. If all are opened together, time to fill the tank completely is:
A) 7 2/7 hours
B) 7 5/7 hours
C) 8 1/7 hours
D) 8 5/7 hours
Answer: B) 7 5/7 hours
Explanation:
- Step 1: Net rate = 1/12 + 1/18 − 1/24
- Step 2: Net rate = (6 + 4 − 3)/72 = 7/72 tank/hr
- Step 3: Remaining part to fill = 1 − 1/4 = 3/4
- Step 4: Time = (3/4) ÷ (7/72) = (3/4)×(72/7) = 54/7
- Final: 54/7 = 7 5/7 hours → option B
Q17): A and B together can complete a work in 60/7 days (i.e., they do 7/60 of work per working day). They start on Day 1, but every 3rd day is a rest day (no work). Total time to finish the work is:
A) 12 2/7 days
B) 12 4/7 days
C) 13 1/7 days
D) 13 4/7 days
Answer: B) 12 4/7 days
Explanation:
- Step 1: Work per working day = 7/60
- Step 2: Working days needed = 1 ÷ (7/60) = 60/7 = 8 4/7 working days
- Step 3: In each 3-day block, working days = 2 (Day 1,2 work; Day 3 rest)
- Step 4: 12 calendar days = 4 blocks ⇒ working days = 8 days
- Step 5: After 12 days, work done = 8 × 7/60 = 14/15, remaining = 1/15
- Final: Extra time on next working day = (1/15) ÷ (7/60) = 4/7 day, so total = 12 4/7 days → option B
Q18): A+B can finish a work in 6 days, B+C in 8 days, and A+C in 12 days. B alone can finish the work in:
A) 8 3/5 days
B) 9 3/5 days
C) 10 3/5 days
D) 12 days
Answer: B) 9 3/5 days
Explanation:
- Step 1: Rates: (A+B)=1/6, (B+C)=1/8, (A+C)=1/12
- Step 2: (A+B) + (B+C) − (A+C) = 2B
- Step 3: 2B rate = 1/6 + 1/8 − 1/12 = (4+3−2)/24 = 5/24
- Step 4: B’s rate = 5/48
- Final: B’s time = 1 ÷ (5/48) = 48/5 = 9 3/5 days → option B
Q19): A, B, and C can complete a work in 40, 60, and 120 days respectively. They work together for some days, then A and B leave. C finishes the remaining work in 20 days. Days for which all three worked together is:
A) 14 2/3 days
B) 15 2/3 days
C) 16 2/3 days
D) 17 2/3 days
Answer: C) 16 2/3 days
Explanation:
- Step 1: C’s 20-day work = 20 × (1/120) = 1/6
- Step 2: So work done before C worked alone = 1 − 1/6 = 5/6
- Step 3: (A+B+C) rate = 1/40 + 1/60 + 1/120 = 1/20
- Step 4: Let together days = x, then x × (1/20) = 5/6
- Step 5: x = (5/6) ÷ (1/20) = (5/6)×20 = 50/3
- Final: 50/3 = 16 2/3 days → option C
Q20): A and B together can complete a work in 9 days, and A alone can complete it in 15 days. They work together for 3 days. Then A becomes 50% more efficient and B becomes 25% less efficient for the remaining work. Total time to finish is:
A) 7 1/2 days
B) 8 days
C) 8 1/2 days
D) 9 days
Answer: B) 8 days
Explanation:
- Step 1: (A+B) rate = 1/9, A’s rate = 1/15
- Step 2: B’s rate = 1/9 − 1/15 = 2/45
- Step 3: Work done in first 3 days together = 3 × 1/9 = 1/3
- Step 4: Remaining work = 1 − 1/3 = 2/3
- Step 5: New A rate = 150% of (1/15) = 1/10
- Step 6: New B rate = 75% of (2/45) = 1/30
- Step 7: New combined rate = 1/10 + 1/30 = 2/15
- Final: Time for remaining = (2/3) ÷ (2/15) = 5 days, total = 3 + 5 = 8 → option B