Q1): A can finish a work in 15 days and B in 20 days. They work together for 4 days, then A leaves. Total days to finish the work is:
A) 13 2/3 days
B) 14 2/3 days
C) 15 2/3 days
D) 16 2/3 days
Answer: B) 14 2/3 days
Explanation:
- Step 1: A’s 1-day work = 1/15, B’s 1-day work = 1/20
- Step 2: Together 1-day work = 1/15 + 1/20 = 7/60
- Step 3: Work done in 4 days = 4 × 7/60 = 7/15
- Step 4: Remaining work = 1 − 7/15 = 8/15
- Step 5: B’s time for remaining = (8/15) ÷ (1/20) = 10 2/3 days
- Final: Total time = 4 + 10 2/3 = 14 2/3 days → option B
Q2): A can do a work in 30 days and B in 40 days. With C, they complete it in 12 days. C alone will complete it in:
A) 24 days
B) 30 days
C) 40 days
D) 60 days
Answer: C) 40 days
Explanation:
- Step 1: (A+B+C) rate = 1/12
- Step 2: A’s rate = 1/30, B’s rate = 1/40
- Step 3: C’s rate = 1/12 − 1/30 − 1/40
- Step 4: C’s rate = 10/120 − 4/120 − 3/120 = 3/120 = 1/40
- Final: C alone time = 40 days → option C
Q3): Pipe A fills a tank in 6 hours and pipe B fills it in 8 hours. An outlet empties it in 12 hours. If all are opened together, the tank will be filled in:
A) 4 1/2 hours
B) 4 4/5 hours
C) 5 hours
D) 5 1/5 hours
Answer: B) 4 4/5 hours
Explanation:
- Step 1: A’s rate = 1/6 tank/hr, B’s rate = 1/8 tank/hr
- Step 2: Outlet empties ⇒ rate = 1/12 tank/hr (subtract)
- Step 3: Net rate = 1/6 + 1/8 − 1/12
- Step 4: Net rate = (4 + 3 − 2)/24 = 5/24
- Final: Time = 1 ÷ (5/24) = 24/5 = 4 4/5 hours → option B
Q4): 12 men can complete a work in 18 days. They work for 6 days, then 6 men leave. Total days to complete the work is:
A) 24 days
B) 27 days
C) 30 days
D) 33 days
Answer: C) 30 days
Explanation:
- Step 1: Total work = 12 × 18 = 216 man-days
- Step 2: Work done in 6 days = 12 × 6 = 72 man-days
- Step 3: Remaining work = 216 − 72 = 144 man-days
- Step 4: Men left = 12 − 6 = 6 men
- Step 5: Days for remaining = 144 ÷ 6 = 24 days
- Final: Total days = 6 + 24 = 30 days → option C
Q5): A can do a work in 18 days and B in 27 days. They work together for some days, then A leaves. B finishes the remaining work in 8 days. For how many days did they work together?
A) 6 3/5 days
B) 7 1/5 days
C) 7 3/5 days
D) 8 days
Answer: C) 7 3/5 days
Explanation:
- Step 1: A’s rate = 1/18, B’s rate = 1/27
- Step 2: Together rate = 1/18 + 1/27 = 5/54
- Step 3: B’s work in 8 days = 8 × (1/27) = 8/27
- Step 4: Remaining work after together days = 8/27
- Step 5: So work done together = 1 − 8/27 = 19/27
- Step 6: Together days = (19/27) ÷ (5/54) = (19/27)×(54/5) = 38/5 = 7 3/5
- Final: Together time = 7 3/5 days → option C
Q6): A and B have efficiency ratio 3:2. Working together, they finish a work in 10 days. A alone will finish it in:
A) 15 days
B) 16 2/3 days
C) 18 days
D) 20 days
Answer: B) 16 2/3 days
Explanation:
- Step 1: Let efficiencies be A = 3x, B = 2x
- Step 2: Together efficiency = 5x ⇒ together rate = 1/10
- Step 3: So 5x = 1/10 ⇒ x = 1/50
- Step 4: A’s rate = 3x = 3/50
- Final: A’s time = 1 ÷ (3/50) = 50/3 = 16 2/3 days → option B
Q7): 15 women can complete a work in 12 days, and 10 men can complete the same work in 9 days. Time taken by 6 men and 10 women together is:
A) 7 2/11 days
B) 8 2/11 days
C) 9 2/11 days
D) 10 2/11 days
Answer: B) 8 2/11 days
Explanation:
- Step 1: Total work = 15×12 = 180 woman-days ⇒ 1 woman’s rate = 1/180
- Step 2: Total work = 10×9 = 90 man-days ⇒ 1 man’s rate = 1/90
- Step 3: Rate of 6 men = 6/90 = 1/15
- Step 4: Rate of 10 women = 10/180 = 1/18
- Step 5: Combined rate = 1/15 + 1/18 = (6+5)/90 = 11/90
- Final: Time = 1 ÷ (11/90) = 90/11 = 8 2/11 days → option B
Q8): A, B, and C can complete a work in 12, 18, and 24 days respectively. They work together for 2 days, then A leaves. Total time to finish the work is:
A) 8 2/7 days
B) 8 4/7 days
C) 9 days
D) 9 1/7 days
Answer: B) 8 4/7 days
Explanation:
- Step 1: Rates: A = 1/12, B = 1/18, C = 1/24
- Step 2: Together rate = 1/12 + 1/18 + 1/24 = 13/72
- Step 3: Work in 2 days = 2 × 13/72 = 13/36
- Step 4: Remaining work = 1 − 13/36 = 23/36
- Step 5: Rate of (B+C) = 1/18 + 1/24 = 7/72
- Step 6: Time for remaining = (23/36) ÷ (7/72) = 46/7 = 6 4/7 days
- Final: Total time = 2 + 6 4/7 = 8 4/7 days → option B
Q9): A and B together finish a work in 8 days, B and C in 12 days, and A and C in 6 days. A alone will finish the work in:
A) 8 3/5 days
B) 9 3/5 days
C) 10 3/5 days
D) 11 3/5 days
Answer: B) 9 3/5 days
Explanation:
- Step 1: (A+B) rate = 1/8, (B+C) rate = 1/12, (A+C) rate = 1/6
- Step 2: Add first two rates: (A+2B+C) = 1/8 + 1/12 = 5/24
- Step 3: Subtract (A+C) = 1/6 = 4/24 ⇒ 2B = 1/24
- Step 4: So B’s rate = 1/48
- Step 5: A’s rate = 1/8 − 1/48 = 5/48
- Final: A’s time = 1 ÷ (5/48) = 48/5 = 9 3/5 days → option B
Q10): A can do 1/5 of a work per day, B can do 1/6 per day, and C can do 1/10 per day. They work in order A, then B, then C, repeating. Time to finish the work is:
A) 6 days
B) 6 1/3 days
C) 6 2/3 days
D) 7 days
Answer: B) 6 1/3 days
Explanation:
- Step 1: Work in 3 days (A+B+C) = 1/5 + 1/6 + 1/10 = 7/15
- Step 2: Work in 6 days (2 cycles) = 2 × 7/15 = 14/15
- Step 3: Remaining work = 1 − 14/15 = 1/15
- Step 4: Next turn is A with rate 1/5
- Step 5: Extra time = (1/15) ÷ (1/5) = 1/3 day
- Final: Total time = 6 + 1/3 = 6 1/3 days → option B
Q11): 18 men can complete a work in 14 days and 21 women can complete the same work in 16 days. Time taken by 6 men and 7 women together is:
A) 20 2/5 days
B) 21 2/5 days
C) 22 2/5 days
D) 23 2/5 days
Answer: C) 22 2/5 days
Explanation:
- Step 1: Total work = 18×14 = 252 man-days ⇒ 1 man’s rate = 1/252
- Step 2: Total work = 21×16 = 336 woman-days ⇒ 1 woman’s rate = 1/336
- Step 3: Rate of 6 men = 6/252 = 1/42
- Step 4: Rate of 7 women = 7/336 = 1/48
- Step 5: Combined rate = 1/42 + 1/48 = (8+7)/336 = 15/336 = 5/112
- Final: Time = 1 ÷ (5/112) = 112/5 = 22 2/5 days → option C
Q12): A is 50% more efficient than B. They complete a work together and get ₹3600. A’s share of money is:
A) ₹1800
B) ₹2000
C) ₹2160
D) ₹2400
Answer: C) ₹2160
Explanation:
- Step 1: 50% more efficient ⇒ A:B efficiency = 3:2
- Step 2: Work share ratio = efficiency ratio = 3:2
- Step 3: Total parts = 3 + 2 = 5
- Step 4: A’s share = (3/5) × 3600
- Final: A’s share = 2160 → option C
Q13): A alone can finish a work in 20 days and B alone in 30 days. A works for 5 days, then B joins A. Total time to finish the work is:
A) 12 days
B) 13 days
C) 14 days
D) 15 days
Answer: C) 14 days
Explanation:
- Step 1: A’s 1-day work = 1/20
- Step 2: Work done by A in 5 days = 5/20 = 1/4
- Step 3: Remaining work = 1 − 1/4 = 3/4
- Step 4: (A+B) rate = 1/20 + 1/30 = 1/12
- Step 5: Time for remaining = (3/4) ÷ (1/12) = 9 days
- Final: Total time = 5 + 9 = 14 days → option C
Q14): Pipe A fills a tank in 5 hours and pipe B in 10 hours. They start together. After 2 hours, an outlet starts which empties the full tank in 20 hours. Total time to fill the tank is:
A) 3 1/5 hours
B) 3 2/5 hours
C) 3 3/5 hours
D) 4 hours
Answer: C) 3 3/5 hours
Explanation:
- Step 1: Initial fill rate (A+B) = 1/5 + 1/10 = 3/10
- Step 2: Work done in first 2 hours = 2 × 3/10 = 3/5
- Step 3: Remaining work = 1 − 3/5 = 2/5
- Step 4: After outlet starts, net rate = 1/5 + 1/10 − 1/20 = 1/4
- Step 5: Time for remaining = (2/5) ÷ (1/4) = 8/5 = 1 3/5 hours
- Final: Total time = 2 + 1 3/5 = 3 3/5 hours → option C
Q15): A and B together can complete a work in 15 days. A alone can do it in 25 days. If A works alone for 5 days and then B joins, total time to finish is:
A) 16 days
B) 17 days
C) 18 days
D) 19 days
Answer: B) 17 days
Explanation:
- Step 1: (A+B) rate = 1/15, A’s rate = 1/25
- Step 2: Work done by A in 5 days = 5/25 = 1/5
- Step 3: Remaining work = 1 − 1/5 = 4/5
- Step 4: Time for remaining with (A+B) = (4/5) ÷ (1/15) = 12 days
- Final: Total time = 5 + 12 = 17 days → option B
Q16): A can do a work in 12 days and B can do it in 16 days. They work alternately: A works for 3 days, then B for 4 days, repeating. Work finishes in:
A) 12 days
B) 13 days
C) 14 days
D) 15 days
Answer: C) 14 days
Explanation:
- Step 1: A’s rate = 1/12, B’s rate = 1/16
- Step 2: Work in A’s 3 days = 3/12 = 1/4
- Step 3: Work in B’s 4 days = 4/16 = 1/4
- Step 4: Work in one full cycle (7 days) = 1/4 + 1/4 = 1/2
- Step 5: Two cycles complete work = 2 × 7 days = 14 days
- Final: Work finishes in 14 days → option C
Q17): A can do a work in 18 days and B in 24 days. With C, they complete it in 9 days. C alone will complete it in:
A) 36 days
B) 48 days
C) 60 days
D) 72 days
Answer: D) 72 days
Explanation:
- Step 1: (A+B+C) rate = 1/9
- Step 2: A’s rate = 1/18, B’s rate = 1/24
- Step 3: C’s rate = 1/9 − 1/18 − 1/24
- Step 4: C’s rate = 8/72 − 4/72 − 3/72 = 1/72
- Final: C alone time = 72 days → option D
Q18): A pipe fills a tank in 12 hours. A leak can empty the full tank in 18 hours. The tank is already 1/3 full. If both are open, time to fill the tank completely is:
A) 18 hours
B) 20 hours
C) 24 hours
D) 30 hours
Answer: C) 24 hours
Explanation:
- Step 1: Fill rate = 1/12 tank/hr
- Step 2: Leak rate (emptying) = 1/18 tank/hr (subtract)
- Step 3: Net rate = 1/12 − 1/18 = (3−2)/36 = 1/36
- Step 4: Remaining part to fill = 1 − 1/3 = 2/3
- Step 5: Time = (2/3) ÷ (1/36) = (2/3)×36 = 24 hours
- Final: Required time is 24 hours → option C
Q19): 30 men can complete a work in 20 days. They work for 10 days normally. Then their efficiency increases by 20% (same men). Total days to finish the work is:
A) 17 1/2 days
B) 18 1/3 days
C) 19 days
D) 20 days
Answer: B) 18 1/3 days
Explanation:
- Step 1: Total work = 30 × 20 = 600 man-days (normal efficiency)
- Step 2: Work done in first 10 days = 30 × 10 = 300 man-days
- Step 3: Remaining work = 600 − 300 = 300 man-days
- Step 4: 20% increase ⇒ effective men = 30 × 1.2 = 36 men
- Step 5: Days for remaining = 300 ÷ 36 = 8 1/3 days
- Final: Total days = 10 + 8 1/3 = 18 1/3 days → option B
Q20): A, B, and C together finish a work in 6 days. A alone can do it in 12 days and B alone in 18 days. C alone will finish it in:
A) 24 days
B) 30 days
C) 36 days
D) 48 days
Answer: C) 36 days
Explanation:
- Step 1: (A+B+C) rate = 1/6
- Step 2: A’s rate = 1/12, B’s rate = 1/18
- Step 3: C’s rate = 1/6 − 1/12 − 1/18
- Step 4: C’s rate = 6/36 − 3/36 − 2/36 = 1/36
- Final: C alone time = 36 days → option C