Time and work Quantitative aptitude questions and answers with general rules

 

As many exams in private sector and public sector Time and Work are important so here we listed  Time and Work  quantitative aptitude questions and answers with general rules

Time and Work

General Rules (or) short cuts
(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.