Q26. A can do a work in 10 days, B in 15 days. If A works alone for 2 days, then B joins, how long will they take to complete the remaining work?
Step 1: Work done by A in 2 days
= 2 × (1/10) = 1/5
Step 2: Remaining work
= 1 − 1/5 = 4/5
Step 3: Combined rate of A and B
= 1/10 + 1/15 = 1/6
Step 4: Time to finish remaining work
= (4/5) ÷ (1/6) = 24/5 = 4.8 days
Final Answer: 4.8 days (or 4 days 19 hours 12 min)
Q27. A and B can do a work in 20 days, B and C in 30 days, and A and C in 40 days. Find how long A, B, and C together will take.
Formula: (A+B) + (B+C) + (A+C) = 2(A+B+C)
Substitution: 1/20 + 1/30 + 1/40 = 2(A+B+C)
LCM = 120 → (6 + 4 + 3)/120 = 13/120
So, 2(A+B+C) = 13/120 → (A+B+C) = 13/240
Time required: 240/13 = 18.46 days
Final Answer: ≈ 18 days 11 hours
Q28. A is 3 times as efficient as B. Together they can do a work in 12 days. How long will B alone take?
Let efficiency of B = 1 unit, so A = 3 units → Total = 4 units.
Work = rate × time → 4 × 12 = 48 units
B’s rate = 1 unit/day → Time = 48/1 = 48 days
Final Answer: 48 days
Q29. 8 men can finish a work in 12 days. How many days will 6 men take?
Formula: M₁D₁ = M₂D₂
Substitution: 8×12 = 6×D₂
D₂ = (8×12)/6 = 16 days
Final Answer: 16 days
Q30. A and B can do a work in 8 days, and B alone can do it in 12 days. How long will A alone take?
Formula: 1/A = 1/Together − 1/B
Substitution: 1/8 − 1/12 = (3−2)/24 = 1/24
Final Answer: 24 days
Q31. A can finish a task in 10 days, B in 20 days, and C in 30 days. If all work together, how long will it take?
Step 1: Combined rate = 1/10 + 1/20 + 1/30
= (6 + 3 + 2)/60 = 11/60
Step 2: Time = 60/11 = 5.45 days
Final Answer: ≈ 5.45 days (5 days 11 hours)
Q32. A alone can complete a job in 8 days. B is 60% as efficient as A. How long will B alone take?
Efficiency ratio: A : B = 100 : 60 = 5 : 3
Time ratio: 3 : 5 inverted → 5 : 3
If A = 8 → B = (5/3)×8 = 13⅓ days
Final Answer: 13⅓ days
Q33. A and B can complete a work in 6 days. A alone can do it in 10 days. Find B’s share of total work.
Formula: 1/B = 1/Together − 1/A
= 1/6 − 1/10 = (5−3)/30 = 2/30 = 1/15
So, B alone → 15 days
Work ratio: A:B = 15:10 = 3:2
Final Answer: B’s share = 2/5 of total work
Q34. A does ¾ of work in 9 days. How long for full work?
Total time = (9 × 1) / (¾) = 9 × 4/3 = 12 days
Final Answer: 12 days
Q35. 6 men can complete a work in 10 days. If 2 men leave after 4 days, how many more days will the remaining men take?
Work done in 4 days: 6×4 = 24 man-days
Total work: 6×10 = 60 man-days
Remaining work: 60−24 = 36
Remaining men = 4 → time = 36/4 = 9 days
Final Answer: 9 more days
Q36. A and B can do a work in 10 days. With C, they complete it in 6 days. How long will C alone take?
Formula: 1/C = 1/Together − 1/A+B
= 1/6 − 1/10 = (5−3)/30 = 2/30 = 1/15
Final Answer: 15 days
Q37. A is twice as good a worker as B. Together they can do a work in 12 days. How long will A alone take?
Efficiency ratio A:B = 2:1 → Time ratio = 1:2
(1/A + 1/(2A)) = 1/12 → (3/2A) = 1/12 → A = 18
Final Answer: 18 days
Q38. A can do a work in 15 days, B in 25 days. They start together, but A leaves after 5 days. How long will B take to finish?
Work done in 5 days: 5(1/15+1/25)=5(8/75)=40/75=8/15
Remaining = 7/15 → B alone rate = 1/25
Time = (7/15) ÷ (1/25) = 175/15 = 11⅔ days
Final Answer: 11⅔ days
Q39. A and B can finish a work in 4 days, and A alone can do it in 6 days. How long will B alone take?
1/B = 1/4 − 1/6 = (3−2)/12 = 1/12
Final Answer: 12 days
Q40. A can do a work in 12 days, B in 16 days, and C in 24 days. Find time taken if all work together.
1/T = 1/12 + 1/16 + 1/24 = (4+3+2)/48 = 9/48 = 3/16
T = 16/3 = 5⅓ days
Final Answer: 5⅓ days
Q41. A can do a piece of work in 12 days, B in 18 days. They start together but A leaves after 4 days. How long will B take to finish the remaining work?
Step 1: Work done in 1 day
A = 1/12, B = 1/18 → A+B = 1/7.2
Step 2: Work done in 4 days
= 4 × 1/7.2 = 4/7.2 = 5/9
Step 3: Remaining work
= 1 − 5/9 = 4/9
Step 4: B’s rate = 1/18 → Time = (4/9) ÷ (1/18) = 8 days
Final Answer: 8 days
Q42. A can do a job in 15 days, B can do it in 20 days. They work together for 5 days, after which A leaves. How long will B take to finish?
Step 1: Combined rate
1/15 + 1/20 = 7/60
Step 2: Work in 5 days
5 × 7/60 = 35/60 = 7/12
Step 3: Remaining
= 1 − 7/12 = 5/12
Step 4: B’s rate = 1/20
Time = (5/12) ÷ (1/20) = 100/12 = 8⅓ days
Final Answer: 8⅓ days
Q43. 4 men can finish a job in 8 days. How many men are needed to do the same work in 4 days?
Formula: M₁D₁ = M₂D₂
4×8 = M₂×4 → M₂ = 8
Final Answer: 8 men
Q44. A can do 1/3 of a work in 5 days. How many days will he take to complete the full work?
Step 1: 1/3 work = 5 days → full work = 5 × 3 = 15 days
Final Answer: 15 days
Q45. A, B, and C can complete a work in 10, 15, and 30 days respectively. How long will they take if all work together?
Step 1: Combined rate
= 1/10 + 1/15 + 1/30 = (3+2+1)/30 = 6/30 = 1/5
Step 2: Time = 5 days
Final Answer: 5 days
Q46. A can do a job in 16 days and B in 12 days. If they work on alternate days starting with A, find total time to complete the work.
Step 1: In 2 days work = (1/16 + 1/12) = (3 + 4)/48 = 7/48
Step 2: Work in 6 such pairs (12 days) = 6×7/48 = 42/48 = 7/8
Step 3: Remaining work = 1/8; next day A works = 1/16
Time = (1/8) ÷ (1/16) = 2 days
Total Time: 12 + 2 = 14 days
Final Answer: 14 days
Q47. A can do a work in 25 days and B in 20 days. They work together for 5 days and then A leaves. In how many more days will B finish the remaining work?
Step 1: Combined work in 1 day = 1/25 + 1/20 = 9/100
Step 2: Work done in 5 days = 45/100 = 9/20
Step 3: Remaining = 1 − 9/20 = 11/20
Step 4: B’s rate = 1/20 → Time = (11/20) ÷ (1/20) = 11 days
Final Answer: 11 days
Q48. 10 men can complete a work in 15 days. How many days will 6 men take to complete the same work?
Formula: M₁D₁ = M₂D₂
10×15 = 6×D₂ → D₂ = 150/6 = 25 days
Final Answer: 25 days
Q49. A can do a piece of work in 8 days and B can do it in 10 days. They work together for 3 days. What fraction of work is left?
Step 1: Combined rate = 1/8 + 1/10 = 9/40
Step 2: Work in 3 days = 3×9/40 = 27/40
Step 3: Remaining work = 1 − 27/40 = 13/40
Final Answer: 13/40 of work remains
Q50. A can do a work in 18 days. B is 50% more efficient than A. Find the time B will take alone.
Step 1: Efficiency ratio = 100 : 150 = 2 : 3
Step 2: Time ratio (inverse) = 3 : 2
Step 3: A’s time = 18 days → B’s time = (2/3)×18 = 12 days
Final Answer: 12 days
No comments:
Post a Comment