Q76. A can do a work in 14 days and B can do the same work in 21 days. How long will they take working together?
1/T = 1/14 + 1/21 = (3 + 2)/42 = 5/42
T = 42/5 = 8.4 days
Final Answer: 8 days 10 hours
Q77. A is twice as fast as B. Together they can do a job in 12 days. Find B’s time alone.
Let B = 1 unit/day, A = 2 units/day ⇒ total = 3 units/day
Work = 3×12 = 36 units
B’s time = 36/1 = 36 days
Final Answer: 36 days
Q78. A can do a work in 16 days, B in 24 days, and C in 48 days. All start together but C leaves after 4 days. Find total time taken.
(A+B+C)’s rate = 1/16 + 1/24 + 1/48 = (3+2+1)/48 = 6/48 = 1/8
Work in 4 days = 4×1/8 = ½
Remaining ½ done by A+B = 1/16 + 1/24 = 5/48
Time = (½)/(5/48) = 24/5 = 4.8 days
Total Time: 4 + 4.8 = 8.8 days (≈ 8 days 19 hrs)
Q79. A can complete a work in 20 days. B can do it in 25 days. A works for 10 days and leaves. Find the remaining work for B.
A’s work in 10 days = 10×(1/20) = ½
Remaining work = 1 − ½ = ½
Final Answer: ½ of the work remains
Q80. A and B together can do a work in 6 days. A alone can do it in 10 days. How many days will B alone take?
1/B = 1/6 − 1/10 = (5−3)/30 = 1/15
Final Answer: 15 days
Q81. A can do a work in 15 days and B can do the same in 25 days. Find their efficiency ratio.
Efficiency ∝ 1/time → A:B = 25:15 = 5:3
Final Answer: 5 : 3
Q82. A can do a work in 12 days, B can do it in 18 days, and C in 36 days. If they work together, how many days will they take?
1/T = 1/12 + 1/18 + 1/36 = (3+2+1)/36 = 6/36 = 1/6
Final Answer: 6 days
Q83. A and B can do a work in 8 days. A alone can do it in 12 days. How many days will B take alone?
1/B = 1/8 − 1/12 = (3−2)/24 = 1/24
Final Answer: 24 days
Q84. 6 men can do a job in 15 days. How many days will 9 men take?
M₁D₁ = M₂D₂ → 6×15 = 9×D₂
D₂ = 10 days
Final Answer: 10 days
Q85. A can do a job in 10 days, B in 20 days. If A works alone for 2 days, how much work remains?
A’s 1-day work = 1/10 → 2 days = 2/10 = 1/5
Remaining = 1 − 1/5 = 4/5
Final Answer: 4/5 work remains
Q86. A can complete a work in 18 days, B is 50% more efficient than A. How long will B take?
Efficiency ratio = 100 : 150 = 2 : 3
Time ratio (inverse) = 3 : 2
A = 18 → B = (2/3)×18 = 12 days
Final Answer: 12 days
Q87. A can complete a work in 9 days, B in 12 days. If they work alternately starting with A, find the total time to finish the work.
2-day work = 1/9 + 1/12 = 7/36
In 5 cycles (10 days) → 35/36 done
Remaining = 1/36 → A’s rate = 1/9 → Time = 1/4 day
Total Time: 10.25 days
Q88. A can do 2/5 of a work in 6 days. Find total time for the whole work.
2/5 → 6 days ⇒ full work = (6 × 5)/2 = 15 days
Final Answer: 15 days
Q89. A can do a work in 12 days. B takes 50% more time. Find B’s time and efficiency ratio.
B’s time = 12×1.5 = 18 days
Efficiency ratio A:B = 18:12 = 3:2
Final Answer: B = 18 days; Ratio 3:2
Q90. A and B together can do a work in 5 days. A alone can do it in 15 days. Find B’s time.
1/B = 1/5 − 1/15 = (3−1)/15 = 2/15 → B = 7.5 days
Final Answer: 7.5 days
Q91. A can do a work in 40 days, B in 60 days. Together they work for 10 days; find the fraction of work left.
1-day work = 1/40 + 1/60 = 5/120 = 1/24
10 days = 10/24 = 5/12 done
Remaining = 7/12
Final Answer: 7/12 remains
Q92. A is 60% as efficient as B. If together they can finish work in 7.5 days, how long will A take alone?
Efficiency ratio A:B = 3:5
Total = 8 parts/day → Work = 8×7.5 = 60
A’s rate = 3 → A’s time = 60/3 = 20 days
Final Answer: 20 days
Q93. A can complete a work in 30 days, B in 20 days, C in 10 days. Find their combined time.
1/T = 1/30 + 1/20 + 1/10 = (1+1.5+3)/30 = 11/60
T = 60/11 = ≈ 5.45 days
Q94. A and B together can do a work in 16 days, B alone in 24 days. How long will A alone take?
1/A = 1/16 − 1/24 = (3−2)/48 = 1/48
Final Answer: 48 days
Q95. A can do a work in 18 days, B in 36 days, C in 72 days. Find the time if all work together.
1/T = 1/18 + 1/36 + 1/72 = (4+2+1)/72 = 7/72
T = 72/7 ≈ 10.3 days
Final Answer: ≈ 10 days 7 hours
Q96. A can do a job in 25 days. B can do the same job in 50 days. They work together for 10 days. What part of work is left?
Combined rate = 1/25 + 1/50 = 3/50
Work in 10 days = 10×3/50 = 3/5
Remaining = 2/5
Final Answer: 2/5 work remains
Q97. A and B together can finish work in 12 days. A alone can do it in 18 days. Find A’s and B’s work ratio.
1/B = 1/12 − 1/18 = 1/36
A:B = (1/18):(1/36) = 2:1
Final Answer: A : B = 2 : 1
Q98. A can complete a work in 8 days, B can do the same in 12 days. If they work on alternate days starting with A, find total time.
2-day work = 1/8 + 1/12 = 5/24
4 cycles (8 days) → 20/24 = 5/6 done
Remaining = 1/6 → A’s rate = 1/8 → time = 4/3 days
Total = 8 + 1.33 = ≈ 9.33 days
Q99. A can do a work in 30 days, B in 40 days, and C in 60 days. All start together but A leaves after 6 days. Find total time.
(A+B+C)’s rate = 1/30 + 1/40 + 1/60 = (4+3+2)/120 = 9/120
Work in 6 days = 6×9/120 = 54/120 = 9/20
Remaining = 11/20; (B+C) = 1/40 + 1/60 = 5/120 = 1/24
Time = (11/20)÷(1/24) = 13.2 days
Total = 6 + 13.2 = 19.2 days
Q100. A can complete a work in 5 days less than B. Together they can do it in 6 days. Find their individual times.
Let B = x days, A = x−5
1/(x−5) + 1/x = 1/6 → (2x−5)/[x(x−5)] = 1/6
Cross-multiply: 12x−30 = x²−5x → x²−17x+30=0
Roots: x=15,2 (reject 2)
B=15 days, A=10 days
Final Answer: A = 10 days, B = 15 days
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