## Time and Work

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## Time and Work: Shortcut Approach

### FORMULAS:

If a person can do a piece of work in n days (hours), then that person’s 1 day’s (hour’s) work is 1/n.
Work done in m days (hours) is m/n.
Total Work = Work done in units per day × Time taken

Q1) A and B can do a piece of work in 6 and 12 days, respectively. They (both) will complete the work in how many days?
1) 9 days
2) 6 days
3) 4 days
4) 18 days

Solution:

Work = LCM(6, 12) = 12 units
Work done in a day: A = a units/day, B = b units/day, C = c units/day
a = 12/6 = 2 units/day; b = 12/12 = 1 units/day
When A and B are working together then work done by A and B in a day is 1 + 2 = 3 units/day
Say the work is completed by A and B (together) in ‘n’ days so, 3n = 12 i.e. n = 4 days

Q2) A does 20% less work than B. If A can complete a piece of work in 7.5 h, then B can do it in
1) 4 h
2) 6 h
3) 8 h
4) 10 h

Solution:

Say, work done by B = 5 units/h so, work done by A = 4 units/h (80% less work than B)
Work = 4(7.5) = 30 units {A does the work in 7.5 h}
Say the work is completed by B in ‘n’ days so, 5n = 30 i.e. n = 6 h

Q3) A can complete a work in 24 days and B can do the same work in 18 days. If A after working for 4 days, leaves the work, find in how many days B will do the remaining work?
1) 10 days
2) 12 days
3) 15 days
4) 16 days

Solution:

Work = LCM(24, 18) = 72 units
Work done in a day: A = a units/day, B = b units/day
a = 72/24 = 3 units/day; b = 72/18 = 4 units/day
Work done by A in 4 days = 3(4) = 12 units
Remaining Work = 72 – 12 = 60 units
Say the work is completed by B in ‘n’ days so, 4n = 60 i.e. n = 15 days

Q4) A can do a piece of work in 50 days and B in 40 days. They work together for 10 days and then A leaves B to finish the work alone. How long will B take to finish it?
1) 11 days
2) 22 days
3) 26 days
4) 18 days

Solution:

Work = LCM(50, 40) = 200 units
Work done in a day: A = a units/day, B = b units/day, C = c units/day
a = 200/50 = 4 units/day; b = 200/40 = 5 units/day
Work done by A and B together in 10 days = (4 + 5)10 = 90 units
Remaining Work = 200 – 90 = 110 units
Say the work is completed by B in ‘n’ days so, 5n = 110 i.e. n = 22 days

Q5) A, B and C can do a piece of work in 12, 18 and 24 days respectively, they work at it together, A stops the work after 4 days and B is called off 2 days before the work is done. In what time is the work finished?
1) 12 days
2) 14 days
3) 16 days
4) 8 days

Solution:

Work = LCM(12, 18, 24) = 72 units
Work done in a day: A = a units/day, B = b units/day, C = c units/day
a = 72/12 = 6 units/day; b = 72/18 = 4 units/day; c = 72/24 = 3 units/day
Say the work is completed in ‘n’ days
A works for 4 days, B for (n – 2) days and C for n days
6(4) + 4(n – 2) + 3n = 72
On solving, n = 8

Q6) A and B can finish a piece of work in 30 days, B and C can finish a piece of work in 40 days, while C and A can finish a piece of work in 60 days. How long will they take to finish it together?
1) 80/3 days
2) 50/3 days
3) 25 days
4) 24 days

Solution:

Work = LCM(30, 40, 60) = 120 units
Work done in a day: A = a units/day, B = b units/day, C = c units/day
a + b = 120/30 = 4 units/day; b + c = 120/40 = 3 units/day; c + a = 120/60 = 2 units/day
On adding the above equations, 2(a + b + c) = 9 i.e. a + b + c = 4.5 units/day
Say the work is completed by A, B and C in ‘n’ days so, 4.5n = 120 i.e. n = 80/3 days