**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?

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.

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?

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?

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.

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.

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