Problems on Time and Work

1) Problem: If 9 men working 6 hours a day can do a work in 88 days. Then 6 men working 8 hours a day

can do it in how many days?

Solution: From the above formula i.e (m1*t1/w1) = (m2*t2/w2)

 so (9*6*88/1) = (6*8*d/1)

 on solving, d = 99 days.

2) Problem: If 34 men completed 2/5th of a work in 8 days working 9 hours a day. How many more man

should be engaged to finish the rest of the work in 6 days working 9 hours a day?

Solution: From the above formula i.e (m1*t1/w1) = (m2*t2/w2)

 so, (34*8*9/(2/5)) = (x*6*9/(3/5))

so x = 136 men

 number of men to be added to finish the work = 136-34 = 102 men

3) Problem: If 5 women or 8 girls can do a work in 84 days. In how many days can 10 women and 5 girls can

do the same work?

Solution: Given that 5 women is equal to 8 girls to complete a work. So, 10 women = 16 girls. Therefore 10

women + 5 girls = 16 girls + 5 girls = 21 girls. 8 girls can do a work in 84 days then 21 girls can do a work in

(8*84/21) = 32 days. Therefore 10 women and 5 girls can a work in 32 days

4) Problem: Worker A takes 8 hours to do a job. Worker B takes 10 hours to do the same job. How long it

take both A & B, working together but independently, to do the same job?

Solution: A's one hour work = 1/8. B's one hour work = 1/10. (A+B)'s one hour work = 1/8+1/10 = 9/40. Both

A & B can finish the work in 40/9 days

5) Problem: A can finish a work in 18 days and B can do the same work in half the time taken by A. Then,

working together, what part of the same work they can finish in a day?

Solution: Given that B alone can complete the same work in days = half the time taken by A = 9 days

 A's one day work = 1/18

 B's one day work = 1/9

 (A+B)'s one day work = 1/18+1/9 = 1/6

6) Problem: A is twice as good a workman as B and together they finish a piece of work in 18 days.In how

many days will A alone finish the work.

Solution: if A takes x days to do a work then B takes 2x days to do the same work

 = > 1/x+1/2x = 1/18

 = > 3/2x = 1/18

 = > x = 27 days.

 Hence, A alone can finish the work in 27 days.