Time and Work — Practice

Question 1

A can do a piece of work in 12 days and B in 18 days. Working together they will finish it in:
(a) 7⅕ days (b) 7½ days (c) 8 days (d) 15 days

Accepted Answer

(a) 7⅕ days.

Work = LCM(12,18) = 36 units. A = 3/day, B = 2/day, together 5/day. Time = 36 ÷ 5 = 7⅕ days.

Question 2

A and B together complete a work in 6 days. A alone can do it in 9 days. B alone will take:
(a) 12 days (b) 15 days (c) 18 days (d) 24 days

Accepted Answer

(c) 18 days.

Work = LCM(6,9) = 18 units. Together = 3/day, A = 2/day, so B = 1/day → 18 days.

Question 3

A is twice as efficient as B, and together they finish a work in 12 days. A alone can finish it in:
(a) 15 days (b) 18 days (c) 20 days (d) 24 days

Accepted Answer

(b) 18 days.

Rates 2 : 1, together 3 units/day. Work = 3 × 12 = 36 units. A alone: 36 ÷ 2 = 18 days.

Question 4

15 men working 8 hours a day finish a work in 20 days. In how many days will 20 men working 6 hours a day finish it?
(a) 18 (b) 20 (c) 22 (d) 24

Accepted Answer

(b) 20 days.

Total effort = 15 × 20 × 8 = 2400 man-hours. New crew supplies 20 × 6 = 120 man-hours daily → 2400 ÷ 120 = 20 days.

Question 5

A can do a work in 12 days, B in 15 days. They start together but A leaves after 4 days. B alone completes the rest in:
(a) 5 days (b) 6 days (c) 7 days (d) 8 days

Accepted Answer

(b) 6 days.

Work = LCM(12,15) = 60 units; A = 5/day, B = 4/day. First 4 days together: 9 × 4 = 36 units. Remaining 24 units at B's 4/day = 6 days.

Question 6

Pipe A fills a tank in 10 hours, pipe B in 15 hours, and pipe C can empty it in 30 hours. With all three open, the empty tank fills in:
(a) 6 hours (b) 7 hours (c) 7.5 hours (d) 8 hours

Accepted Answer

(c) 7.5 hours.

Tank = LCM(10,15,30) = 30 units. Rates: +3, +2, −1 → net +4 units/hour. Time = 30 ÷ 4 = 7.5 hours.

Question 7

3 men or 5 women can complete a work in 12 days. In how many days will 6 men and 5 women complete it?
(a) 4 (b) 5 (c) 6 (d) 8

Accepted Answer

(a) 4 days.

3 men = 5 women, so 1 man = 5/3 women. The crew 6m + 5w = 10w + 5w = 15 women. Total work = 5 women × 12 days = 60 woman-days → 60 ÷ 15 = 4 days.

Question 8

A can do a job in 10 days and B in 15 days. They work together and are paid ₹1500 in all. A's share is:
(a) ₹600 (b) ₹750 (c) ₹900 (d) ₹1000

Accepted Answer

(c) ₹900.

Wages divide by work done, i.e., by rates: 1/10 : 1/15 = 3 : 2. A's share = 1500 × 3/5 = ₹900.

Question 9

A and B can do a work in 12 days, B and C in 15 days, C and A in 20 days. Working together, all three finish it in:
(a) 8 days (b) 10 days (c) 12 days (d) 15 days

Accepted Answer

(b) 10 days.

Work = LCM(12,15,20) = 60 units. Pair rates: 5, 4, 3 units/day; their sum 12 counts everyone twice, so A+B+C = 6 units/day. Time = 60 ÷ 6 = 10 days.

Question 10

A alone finishes a work in 9 days, B alone in 12 days. They work on alternate days with A starting. The work is completed in:
(a) 10 days (b) 10¼ days (c) 10½ days (d) 11 days

Accepted Answer

(b) 10¼ days.

Work = LCM(9,12) = 36 units; A = 4/day, B = 3/day. Each (A,B) cycle = 7 units in 2 days. Five cycles = 35 units in 10 days. Day 11 is A's turn: 1 unit remains at 4 units/day = ¼ day. Total = 10¼ days.

Practice — Time and Work

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