A and B together finish a job in 6 days, and A alone takes 9 days. How long will B alone take?
B = 1/6 − 1/9 = (3 − 2)/18 = 1/18
B alone = 18 days
Answer: 18 days
Time and Work · Exercise 1 of 5
40 time and work questions at competitive-exam level: combined rates, pairs of workers, efficiency comparisons, alternate days, leaving early, work and wages. Every solution uses the LCM (unit) method one step per line.
A and B together finish a job in 6 days, and A alone takes 9 days. How long will B alone take?
B = 1/6 − 1/9 = (3 − 2)/18 = 1/18
B alone = 18 days
Answer: 18 days
A can finish a job in 16 days, and B is 60% more efficient than A. How long will B alone take?
B's rate = 1.6 × A's
B's time = 16 ÷ 1.6 = 10 days
Trap: 9.6 days takes 40% off the time.
Answer: 10 days
A can do a job in 20 days and B in 30 days. They work together for 5 days, and A finishes the rest alone. How long does A take for the rest?
Job = 60 units; A = 3, B = 2 a day
5 days together = 25 units → 35 left
A takes 35 ÷ 3 = 11⅔ days
Answer: 11⅔ days
A can finish a job in 6 days and B in 12 days. They finish it together and are paid ₹ 1,800. What is A's share?
Wages ∝ work done ∝ rate
A : B = 1/6 : 1/12 = 2 : 1
A = 2/3 × 1,800 = ₹ 1,200
Trap: ₹ 600 splits in the ratio of days.
Answer: ₹ 1,200
A can finish a job in 15 days and B in 20 days. What fraction of the job is left after they work together for 4 days?
Job = 60 units; A = 4, B = 3 → 7 a day
4 days = 28 units
Left = 32/60 = 8/15
Trap: 7/15 is the part done.
Answer: 8/15
Ravi does one-third of a job in 6 days, and Kiran does three-fifths of it in 18 days. How long will they take to finish the job together?
Ravi alone = 18 days; Kiran alone = 30 days
Job = 90 units; Ravi 5, Kiran 3 a day
Days = 90 ÷ 8 = 11.25
Answer: 11.25 days
A and B can finish a job in 12 days. With C's help they finish it in 8 days. How long would C alone take?
C = 1/8 − 1/12 = (3 − 2)/24 = 1/24
C alone = 24 days
Answer: 24 days
A can finish a job in 8 days and B in 12 days. They work on alternate days, A starting. In how many days is the job finished?
Job = 24 units; A = 3, B = 2 a day
Each 2-day pair = 5 units
4 pairs (8 days) = 20 units
Day 9 (A): 23 units; day 10 (B) needs 1 unit = half a day
Total = 9½ days
Trap: 10 days forgets the half day.
Answer: 9½ days
A worker plans to finish a job in 15 days, but he works at only 80% of the planned speed. How many extra days does he need?
Time ∝ 1/speed
Actual time = 15 ÷ 0.8 = 18.75 days
Extra = 3.75 days
Trap: 20% of 15 = 3 days treats it as direct.
Answer: 3.75 days
A takes 3 days more than B to finish a job, and together they take 2 days. How long does A alone take?
Let B = x, A = x + 3
1/x + 1/(x + 3) = 1/2
x² − x − 6 = 0 → x = 3
A = 6 days
Answer: 6 days
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