Chapter 11: TIME AND WORK


Introduction


If A can do a work in 'n' days then he does 1/n work daily. If A is thrice as good as B at something then the ratio of their work done is 1:3.

Questions & Answers


Q. Worker A takes 8 hours to do a job. Worker B takes 10 hours to do the same Job.How long should it take both A and B, working together but independently, to do the same job?

A. A does 1/8 work in an hour and B does 1/10 so both do (1/8 + 1/10) in one hour. 18/80 work in an hour so they need 80/18 to do the work completely.




Q. A and B together can complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete that work? 

A. A can do 1/12 in a day, B can do 1/x. (1/12 + 1/x) = 1/4 from given data. Solving it we get value of x.


Q. A can do a piece of work in 7 days of 9 hours each and B can do it in 6 days of 7 hours each. How long will they take to do it, working together 8 hours a day?

A. A can do work in 63 hrs so 1/63 per hour. B can do work in 42 hrs so 1/42 per hour. Both can do work in (1/63 + 1/42) = (2+3/126) = 5/126 work in 1 hr so they need 126/5 hrs or 25.2 hrs so if 8 hrs / day are taken then 4 days.




Q. A and B can do a piece of work in 18 days; B and C can do it in 24 days A and C can do it in 36 days. In how many days will A, Band C finish it together?

A. A and B can do 1/18 work per day; B and C can do 1/24 work per day; A and C can do 1/36 work per day.

Adding all three we get 2(A+B+C) = (4+3+2)/72 = 1/8 work per day or 8 days to do work together.




Q. A can do a certain job in 12 days. B is 60% more efficient than A. How many days does B alone take to do the same job?

A. B is 60% more efficient than A so if B takes 100 hrs then A needs 160 hrs so time taken ratio of A : B = 160 : 100 = 8 : 5.

B's time = A's time * 5 / 8 = 12 * 5 / 8 = 7 1/2 days.


Q. A can do a piece of work in 80 days. He works at it for 10 days B alone finishes the remaining work  in 42 days.  In how much  time will A and B working  together,  finish  the work?

A. A does 1 / 80 work in 1 day and so 10/80 work in 10 days. 70/80 work is left.

B does 70/80 work in 42 days so in 1 day he does  70 /42 * 80 = 1 / 48 work.

A and B together do (1/80 + 1/48) in one day. Reciprocal of result will give total days needed.




Q. 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.

A. A, B, C do (1/6 + 1/8 + 1/x) = 1/3 so 1/x = 1/3 - 1/6 - 1/8

= (8 - 4 - 3) / 24

= 1/24 work per day so C can finish job in 24 days.

So ratio of 1 days work is = 1/6 : 1/8 : 1/24 = 4:3:1 . This can be used to get their share of the money.


Q. A and B working separately can do a piece of work in 9 and 12 days respectively, If they work for a day alternately, A beginning, in how many days, the work will be completed?

A. A work in 1 day is 1/9 and B's work is 1/12 so since they work alternately in 2 days work by them is (1/9+1/12) = (4+3)/36 = 7/36.

Work done in 10 days is = 7/36 * 5 = 35/36.

On last day A's turn and 1/36 work remains which A can do in 1/4 day. Total days needed are 10 1/4 days.




Pipes and Cisterns


If a pipe can fill a tank in 'x' hours then in 1 hour it can fill 1/x. If a pipe can empty a tank in y hours then in 1 hour it can empty 1/y.


If one pipe fills a tank in 'x' hrs and second pipe empties it in 'y' hrs then in 1 hour net part filled is 1/x - 1/y (x>y).


If one pipe fills a tank in 'x' hrs and second pipe empties it in 'y' hrs then in 1 hour net part filled is 1/y - 1/x (y>x).




Questions & Answers


Q. Two pipes  can  fill  a  tank  in  10 hours  and  12 hours  respectively while  a third,  pipe  empties  the  full  tank  in  20  hours.  If  all  the  three  pipes  operate simultaneously, in how much time will the tank be filled?

A. Total work by all pipes together = (1/10 + 1/12 - 1/20) = (6+5-3)/60 = 2/15

So it takes 7.5 hrs to fill tank.


Q. Two pipes can fill a cistern in 14 hours and 16 hours respectively. The pipes are  opened  simultaneously  and  it  is  found  that  due  to  leakage  in  the  bottom  it  took  32 minutes more to fill the cistern.When the cistern is full, in what time  will the leak empty it?

A.Pipe A and B can fill tank in (1/14 + 1/16) = (8+7)/112 = 15/112 work in 1 hr. So total time needed is 112/15 i.e. 7 hrs 28 mins. But when leak is there it took 32 mins more so 8 hrs.

15/122 - 1/x = 1/8 so we can get value of x.


Q. Two pipes A and B can fill a tank  in 36 min. and 45 min. respectively. A water pipe C  can  empty  the  tank  in  30 min.  First A  and  B  are  opened.  after  7 min, C  is  also opened. In how much time, the tank is full?

A. A and B can together fill in 1 min = (1/36 + 1/45) = (5+4)/180 = 1/20 so in 7 mins 7/20 is filled. Remaining 13/20 will be filled by all three.

(1/36 + 1/45 - 1/30) = (5+4- 6)/180 = 3/180 = 1/60. So they need to fill 13/20 or 39/60. Which they can do in 39 mins as they do 1/60 in 1 min.




Q. Two pipes A,B can fill a tank in 24 min. and 32 min. respectively. If both the pipes are opened simultaneously, after how much time B should be closed so that the tank is full in 18 min.?

A. Suppose B is closed in 'x' min.

Part of tank filled in 'x' min by both + part of tank filled in (18-x) min by A = 1.

x  * ( 1/24 + 1/32) + (18-x) * (1/24) = 1 Solving this we can get 'x'.


CAT Problems



Q.Three machines, A, B and C can be used to produce a product. Machine A will take 60 hours to produce a million units. Machine B is twice as fast as Machine A. Machine C will take the same amount of time to produce a million units as A and B running together. How much time will be required to produce a million units if all the three machines are used simultaneously?


  1. 12 hours
  2. 10 hours
  3. 8 hours
  4. 6 hour

Ans.b


Q.Two towns A and B are 100 km apart. A school is to be built for 100 students of town B and 30 students of Town A. Expenditure on transport is Rs. 1.20 per km per student. If the total expenditure on transport by all 130 students is to be as small as possible, then the school should be built at


  1. 33 km from Town A.
  2. 33 km from Town B
  3. Town A
  4. Town B

Ans.d


Q.One man can do as much work in one day as a woman can do in 2 days. A child does one third the work in a day as a woman. If an estate-owner hires 39 pairs of hands, men, women and children in the ratio 6 : 5 : 2 and pays them in all Rs. 1,113 at the end of the days work. What must the daily wages of a child be, if the wages are proportional to the amount of work done?


  1. 14
  2. 5
  3. 20
  4. 7

Ans.d


Q.A water tank has three taps A, B and C. A fills four buckets in 24 minutes, B fills 8 buckets in 1 hour and C fills 2 buckets in 20 minutes. If all the taps are opened together a full tank is emptied in 2 hours. If a bucket can hold 5 litres of water, what is the capacity of the tank?


  1. 120 litres
  2. 240 litres
  3. 180 litres
  4. 60 litres

Ans.b

Time and work - CAT problems


Q.Three bells chime at an interval of 18 min, 24 min and 32 min. At a certain time they begin to chime together. What length of time will elapse before they chime together again?


  1. 2 hr and 24 min
  2. 4 hr and 48 min
  3. 1 hr and 36 min
  4. 5 hr

Ans.b


Q.Two typists undertake to do a job. The second typist begins working one hour after the first. Three hours after the first typist has begun working, there is still 9/20 of the work to be done. When the assignment is completed, it turns out that each typist has done half the work. How many hours would it take each one to do the whole job individually ?


  1. 12 hr and 8 hr
  2. 8 hr and 5.6 hr
  3. 10 hr and 8 hr
  4. 5 hr and 4 hr

Ans.c


Q.A group of men decided to do a job in 8 days. But since 10 men dropped out every day, the job got completed at the end of the 12th day. How many men were there at the beginning?


  1. 165
  2. 175
  3. 80
  4. 90

Ans.a


Q. A company has a job to prepare certain number cans and there are three machines A, B and C for this job. A can complete the job in 3 days, B can complete the job in 4 days, and C can complete the job in 6 days. How many days will the company take to complete the job if all the machines are used simultaneously?


  1. 4 days

  2. 4/3 day

  3. 3 days

  4. 12 days


Ans . b


Q. Two full tanks, one shaped like a cylinder and the other like a cone, contain jet fuel. The cylindrical tank holds 500 L more than the conical tank. After 200 L of fuel has been pumped out from each tank the cylindrical tank contains twice the amount of fuel in the conical tank. How many litres of fuel did the cylindrical tank have when it was full?


  1. 700 L

  2. 1,000 L

  3. 1,100 L

  4. 1,200 L


Ans . D


Read and Answer


There are three bottles of water — A, B, C, whose capacities are 5 L, 3 L, and 2 L respectively. For transferring water from one bottle to another and to drain out the bottles, there exists a piping system. The flow through these pipes is computer-controlled. The computer that controls the flow through these pipes can be fed with three types of instructions, as explained below.

time and work problems CAT

Initially, A is full with water, and B and C are empty.


Q. After executing a sequence of three instructions, bottle A contains one liters of water. The first and the third of these instructions are shown below.
First instruction: FILL (C, A)
Third instruction: FILL (C, A)
Then which of the following statements about the instructions is true?


  1. The second instruction is FILL (B, A).

  2. The second instruction is EMPTY (C, B)

  3. The second instruction transfers water from B to C

  4. The second instruction involves using the water in bottle A.


Ans . B


Q. Consider the same sequence of three instructions and the same initial state mentioned above. Three more instructions are added at the end of the above sequence to have A contain 4 L of water. In this total sequence of six instructions, the fourth one is DRAIN (A). This is the only DRAIN instruction in the entire sequence. At the end of the execution of the above sequence, how much water is contained in C?


  1. 1 L

  2. 2 L

  3. 0

  4. None of these


Ans . C


Q. A can complete a piece of work in 4 days. B takes double the time taken by A, C takes double that of B, and D takes double that of C to complete the same task. They are paired in groups of two each. One pair takes two-thirds the time needed by the second pair to complete the work. Which is the first pair?


  1. A and B

  2. A and C

  3. B and C

  4. A and D


Ans . D


Q. Two men X and Y started working for a certain company at similar jobs on January 1, 1950. X asked for an initial salary of Rs. 300 with an annual increment of Rs. 30. Y asked for an initial salary of Rs. 200 with a rise of Rs. 15 every 6 months. Assume that the arrangements remained unaltered till December 31, 1959. Salary is paid on the last day of the month. What is the total amount paid to them as salary during the period?


  1. Rs. 93,300

  2. Rs. 93,200

  3. Rs. 93,100

  4. None of these


Ans . A


Quiz

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