TIME AND WORK
Introduction;
This chapter deals with problems related
with time and work done by person.
Important points and formula;
1. If ‘A ‘can finish a piece of work in ‘n’ days then A s 1
day’s work is =1\n
2. If A is X-times as good a workman as B. then A will take
1\x of the time that B –takes to do a certain work.
3.If M1 person can do W1 times in D1 days for T1 hours and M2
person works in D2 days for T2 hours then=M1D1T1W2=M2D2T2W1
4. If A can finish a work in X-days and B can finish the some
work in Y- days then live taken by both to finish the work are xy\X+Y days
5. If A and B together can do a piece of work in X- days and
A alone can do it in Y- days then B alone can do it XY\Y-Z days.
6. If A,B and C can do a work in X,Y and Z days respectively
then all of them working together can finish the work in (XYZ)/(XY+YZ+ZX)
7. If two taps A and B take a and b hours respectively to
fill a tank then the two taps together fill 1/a+1/b part of the tank in an hour
and the total tank fill in ab/a+b hours.
Solved examples
1.’A’ can do a piece of work in 12 days and ‘B’ alone can it
in 15 days how much time both will take to finish the work together?
Sol.
Work done
by’A’ in 1 day =1/12
Work done
by’b’ in 1 day =1/15
There fore both together can finish the mork in 20/3days or
6 2/3days.
Short cut: xy/x+y=12*15/12+15=12*15/27=20/3=6 2/3days.
2. A tank can be filled separately by the two pipes in 12
and 16 minutes respectively if both pipes are opend together, when will the
tank be filled?
Short cut: the time taken to fill the tank by both pipe
ab/a+b=12*6/12+16=12*16/28=48/7=6 6/7 minutes
3.16 men can do a piece work in ten days. How many men are
needed to complete the work in 40 days?
M1 D1=M2 D2 => M2=M1 D1/D2=16*10/40=4men
4. A and B can do a piece of work in 18 days. B and C in 24
days. A and C in 36 days. In what time can they do it in all work together?
Sol: [(A+B) + (B+C) + (A+C)]‘ s 1day’s
work=1/18+1/24+1/36=18
2(A+B+C)’s 1 day
work=1/8
(A+B+C)’s 1 day
work=1/16
There fore all can finish the work in 16 days.
Solve the Problems
1.A takes twice as much time as B or thrice as much time to finish a
piece of work ,working together they can finish the work in 2 days, can do the
work alone in
a) 4 days b) 6 days
c) 12 days d) 15 days
2. X and Y can do a piece of work in 20 days and 12 days respectively.
X started the work alone and then after 4 days Y joined him till the completion
of work. How long did the work left?
a) 6 days b) 10 days c) 15 days
d) 20 days
3. A,B and C can do a piece of work in 20 , 30 and 60 days
respectively. In how many days A do the work if the A is assisted by B and C on
every third day?
a) 12 days b) 15 days c) 16 days
d) 18 days
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