# Time And Work

Posted on 4:05 AM in

Time & Work

General Rules
(i) If A can do a piece of work in n days, then A's 1 day's work = 1/n.

(ii) If A's 1 day's work = 1/n, then A can finish the work in n days.
(ii) If A is thrice as good a workman as B, then:
Ratio. of work done by A and B = 3 : 1,
Ratio of times taken by A & B to finish a work = 1 : 3.
Solved Problems
Ex. 1.A can do a piece of work in 10 days which B alone can do in 12
days. In how many days will they finish the work, both working together?

Sol. A's 1 day's work = 1/10, B's 1 day's work = 1/12
(A + B)'s 1 day's work = (1/10 +1/12)= 11/60
:. Both will finish the work in 60/11= 5 5/11days.

Ex. 2. Two persons A and B working together can dig a trench in 8 hours while A alone can dig it in 12 hours. In how many hours B alone can dig such a trench?

Sol. (A + B)'s 1 hour's work = 1/8, A's 1 hour's work = 1/12
:. B's 1 hour's work=(1/8-1/12 )=1/24
Hence B alone can dig the trench in 24 hours.

Ex.3. A and B can do a piece of work in 12 days; Band C can do it
in 15 days ; A and C can do it in 20 days. In how many days will A, Band' C finish it, working all together?Also ,find the number of days taken by each to finish it working alone.

Sol. (A+B)'s 1 day's work =1/12; (B+C)'s 1 day's work = 1/15
and (A + C)'s 1 day's work = 1/20
Adding, we get: 2 (A + B + C)'s 1 day's work =(1/12 + 1/15 + 1/20)= 1/5
:. (A + B + C)'s 1 day's work =1/10
Thus, A, Band C together can finish the work in l0 days.
Now, A's 1 day's work
= [(A + B + C)’s 1 day's work] - [(B + C)'s 1 day's work]
=(1/10 – 1/15) = 1/30
:.   A alone can finish the work in 30 days.
Similarly, B's 1 day's work =(1/10 – 1/20)= 1/20
:. B alone can finish the work in 20 days.
And, C's 1 day's work=(1/10 – 1/12)= 1/60 .
:.   C alone can finish the work in 60 days.
Ex. 4. 3 men can complete a piece of work in 6 days. Two days after
they started the work, 3 more men joined them. How many days will they take to complete the remaining work?
Sol. Work done by 3 men in 2 days = (1/6x 2 )=1/3.
Remaining work = (1 – 1/3)= 2/3
Now 3 men's 1 day's work =1/6
1 man's 1 day's work = 1/18
6 men's 1 day's work = (6 x 1/18=1/3
Now, 1/3 work is done by them in 1 day.
:. 2/3 work is done by them in (3 x2/3)= 2 days.
Ex. 5.2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days. In how many days can 2 men and 1. boy do the work? .

Sol. Let 1 man's 1 day's work = x &.1 boy's 1 day's work = y.
Then, 2x+3y=1/10 and3x+2y= 1/8
Solving, we get: x = 7/200 and y = 1/100
:.' (2 men + 1 boy)'s 1 day's work = (2 x 7/200+ 1 x 1/100)= 16/200 =         2/25
So, 2 men & 1 boy together can finish the work in 25/2 = 121/2 days.
Ex. 6. 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?

Sol. (A's 1 day's work) : (B's 1 day's work) = 2: 1.
(A + B)'s 1 day's work =1/18.
Divide 1/18 in the ratio 2 : 1.
:. A's 1 day's work = [1/18 X 2/3] = 1/27
Hence, A alone can finish the work in 27 days.

Ex.7. A and B undertake to do a piece of work for Rs. 600. A alone
can- do it in 6 days while B alone can do it in 8 days. With the help of C, they finish it in 3 days. Find the share of each.

Sol. C’s 1 day s work = 1/3 – [1/6 + 1/8]= 1/24
:. A: B : C = Ratio of their 1 day's work = 1/6 : 1/8 : 1/24 = 4:3:1
:. A's share=Rs(600X4/8)=Rs.300,
B's share = Rs. (600 x 3/8)= Rs. 225.
C’s share = Rs. [600 - (300 + 225)] = Rs. 75.