**SSC CHSL Topic Wise Study Material – Quantitative Aptitude – Time and Work**

Contents

SSC CHSL Study MaterialSSC CHSL Previous PapersSSC CHSL Practice Workbook

This chapter is consist of two different topics i.e., ‘Time and Work’ and ‘Pipe and Cistern’.

Problems from this chapter are solved with the help of the concept used in elementary algebra. The concept is called unitary method.

**Unitary Method** This is a technique used for solving a class of problems in variation. It consists of altering one of the variable to a single unit, i.e., 1 and then performing the operation necessary to alter it to the desired value.

**Basic Assumption of Work and Time**

X. How to calculate the required number of persons to complete a particular work in a stipulated time period ?

Y. How to calculate the required time to complete a particular work by certain number of persons ?

To find X and Y the 1st and foremost task is to keep following basic points in mind.

• While solving problems, the work done is always supposed to be equal to 1.

• If a person can do a piece of work in n days, then that person’s 1 day’s work = 1/n.

• If a person’s 1 days’s work = 1/n, then the person will complete the work in n days.

• A person works equally every day.

**Some Useful Facts/Formulae**

• If A can do a piece of work in X days and B can do the same work in Y days, then both of them working together will do the same work in XY/X + Y days.

**Example A can finish a piece of work by working alone in 6 days and B, while working alone, can finish the same work in 12 days. If both of them work together, then in how many days, the work will be finished?**

(a) 4 days

(b) 6 days

(c) 9 days

(d) 12 days

• If A, B and C, while working alone can complete a work in X, Y and Z days, respectively, then they will together

complete the work in XYZ/XY + YZ + ZX days.

• Two persons A and B, working together can complete a piece of work in X days. If A, working alone, can complete the work in Y days, then B, working alone,will complete the work in XY/Y-X days

**Example A and B together can do a piece of work in 12 days, while B alone can finish it in 30 days. A alone can finish the work in SSC (1o+2) 2010**

(a) 15 days

(b) 18 days

(c) 20 days

(d) 25 days

**Example If A and B together can complete a piece of . work in 15 days and B alone in 20 days, in how many days can A alone complete the work? ssc (10+2) 2010**

(a) 60

(b) 45

(c) 40

(d) 30

• If A and B, working together can finish a piece of work in X days, B and C in Y days, C and A in Z days, then

(a) A, B and C working together, will finish the job in

(2XYZ/XY + YZ + ZX)days

**Example If A and B together can finish a piece of work in 20 days, B and C in 10 days and C and A in 12 days, then A, B and C jointly can finish the same work in SSC (10 + 2)2011**

(a) 4 2/7 days

(b) 30 days

(c) 8 4/7 days

(d) 7/60 days

(b) If A and B working together can finish a work in X days and A is k time efficient than B then the time taken by

(i) B, working alone to complete the work is (k + 1) X.

(ii) A, working alone to complete the work is (k + 1/k)X.

**Example A and B can do a job together in 12 days. A is 2 times as efficient as B. In how many days can B alone complete the work? SSC(10+2) 2012**

(a) 36

(b) 12

(c) 18

(d) 9

• If M1 persons can do W1 work in D1 days working T1 h in a day and M2 persons can do W2 work in D2 days working T2 h in a day, then we have a very basic and all in one relationship as M1D1T1W2 =M2D2T2W1

**Example 16 men can do a piece of work in 10 days. How many men are needed to complete the work in 20 days?**

(a) 4 men

(b) 6 men

(c) 8 men

(d) 9 men

**Pipe and Cisterns**

**Inlet Pipe** It fills a tank/cistern/reservoir. In other words, an inlet pipe sends water into a tank/cistern/reservoir.

**Outlet Pipe** It makes tank/cistern/reservoir empty. In other words, an outlet pipe sends water out of a tank/ cistern/reservoir.

**Basic Principles of Pipe and Cistern**

* If a pipe fills a tank in m h, then the part of tank filled in 1 h = 1 / m.

* If a pipe makes a tank empty in n h, then the part of tank emptied in 1 h = 1/n

* If a pipe fills 1/m part of a tank in 1 h, then the time taken by pipe to fill full tank = m h

* If a pipe makes empty 1/n part of a tank in 1 h, then the time taken by pipe of empty full tank =n h.

* Generally, time taken to fill a tank is taken in positive (+ ve) value and time taken to empty a tank is taken in negative(-ve) value.

**Some Useful Facts/Formulae**

• Two pipes A and B can fill (or empty) a cistern in X and Y h, respectively while working alone. If both the pipes are opened together, then the time taken to fill (or empty) the cistern is given by

(XY/X+Y)h

• Three pipes A, B and C can fill a cistern in X, Y and Z h, respectively, while working alone. If all the three pipes are opened together, the time taken to fill the cistern is

(X x Y x Z/XY + YZ + ZX)h

• A tank takes X h to be filled by a pipe. But due to a leak, it is filled in Y h. The amount of time in which the leak can empty the full tank = (XY/Y-X)h

• Two pipes A and B can fill a cistern in X h and Y h, respectively. There is also an outlet C. If all the three pipes are opened together, the tank is full in Z h. The time taken by C to empty the full tank is given by

(XYZ/XZ+YZ-XY)h

**Essential Points**

**Reference Corner**

**1. Piyush has done 1/3rd of a job in 30 days, Sanjeev completes the rest of the job in 60 days. In how many days can they together do the job? SSC (10 + 2) 2017**

(a) 15

(b) 45

(c) 30

(d) 10

**2. A and B can do a piece of work in 15 days. B and C can do the same work in 10 days and A and C can do the same in 12 days. Time taken by A, B and C together to do the job is SSC (10 + 2) 2015**

(a) 9 days

(b) 8 days

(c) 4 days

(d) 5 days

**3.One man or two women or three boys can do a piece of work in 88 days. One man, one woman and one boy will do it in SSC (10 + 2) 2014**

(a) 48 days

(b) 20 days

(c) 44 days

(d) 24 days

**4. Two Pipes A and B can separately fill a tank in 2 h and 3 h respectively. If both the pipes are opened simultaneously in the empty tank, then the tank will be filled in SSC (10+2) 2014**

(a) 1 h 15 min

(b) 1 h 20 min

(c) 1 h 12 min

(d) 2 h 30 min

**5.A and B working separately can do a piece of work in 9 days and 15 days respectively. If they work for a day alternately, with A beginning, then the work will be completed in SSC (10 + 2) 2014**

(a) 10 days

(b) 11 days

(c) 9 days

(d) 12 days

**6. Two Pipes A and B can fill a tank in 36 min and 45 min respectively. Another Pipe C can empty the tank in 30 min. First A and B are opened. After 7 min, C is also opened. The tank is filled up in SSC (10 + 2) 2014**

(a) 39 min

(b) 46 min

(c) 40 min

(d) 45 min

**Practice Exercise**

**1. A work is to be completed in 92 days and 224 men were set to work, each working 16 h a day. After 66 days, 4/7 of the ****work is completed. How many additional men may be employed so that the work may be completed in time, each man now working 18 h a day?**

(a) 162

(b) 234

(c) 262

(d) 81

**2. 12 engines consume 30 metric tonne of coal when each is running 18 h a days. How much Coal will be required for 16 engines, each running 24 h a day, it being given that 6 engines of former type consume as much as 8 engines of latter type?**

(a) 20 tonne

(b) 30 tonne

(c) 60 tonne

(d) 40 tonne

**3. A garrison 6600 men had provisions for 64 days at the rate of 1700 g per head. At the end of 14 days, a reinforcement arrives and it was found that the provision will last 34 days more at the rate of 1650 g per head. What is the strength of the inforcement?**

(a) 3400

(b) 6800

(c) 3300

(d) 3500

**4. A can do 3/4 part of a work in 18 days. B can do 2/3 part of the lane work in 12 days and C can do 60% of the lane work in 24 days. If A, B and C do the work alone for 4 days, 6 days and 8 days, respectively. What per cent of work is remaining?**

(a) 40

(b) 25

(c) 30

(d) 27

**5. If 12 men and 16 boys can do a piece of work in 5 days; 13 men and 24 boys can do it in 4 days, then the ratio of the daily work done by a man to that of a boy is**

(a) 2 : 1

(b) 3 : 1

(c) 2 : 3

(d) 5 : 4

**6. A and B can complete a piece of work in 15 days and 10 days, respectively. They contracted to complete the work for Rs 30000. The share of A in the contracted money will be .**

(a) Rs 18000

(b) Rs 16500

(c) Rs 12500

(d) Rs 12000

**7. How much will a man earn at Rs 3 an hour who start of 8 am and finishes at 5 pm haying rested for two intervals of half an hour each?**

(a)Rs 24

(b)Rs 27

(c)Rs 36

(d)Rs 39

**8. If A, B and C earn Rs 150 per day while A and C earn Rs 94 per day and B and C earn Rs 76 per day, then C’s earning per day is**

(a)Rs 56

(b)Rs 75

(c)Rs 20

(d)Rs 34

**9. If two pipes function together, the tank will be filled up in 12 h. One pipe fills the tank in 10 h faster than the other. How many hours does the faster pipe take to fill up the tank?**

(a) 30 h

(b) 60 h

(c) 15 h

(d) 25 h

**10. Three taps A, B and C fill tank in 20 min, 15 min and 12 min, respectively. If all the taps are opened simultaneously, how long will they take to fill 40% of the drum?**

(a) 1 min

(b) 2 min

(c) 3 min

(d) 4 min

**11. If 5 men can do a piece of work in 6 days and 10 women can do it in 5 days, in how many days can 3 men and 5 women do the same piece of work?**

(a) 3 days

(b) 6 days

(c) 5 days

(d) 4 days

**12.A does 2/5 of a work in 9 days; he then calls in B and they together complete the work in 6 days. How long would B alone have taken to complete the work?**

(a) 10 days

(b) 6 12/13 days

(c) 8 2/11 days

(d) 18 days

**13.A water tank of 1000 L capacity is connected to a tap which can fill it at the rate of 20 L per minute and water is let out at the same time at the rate of 5 L per minute. After an hour the outlet is shut off. Find how long will it take now for the tank to become full?**

(a) 7 1/2 min

(b) 5 min

(c) 6 min

(d) 10 min

**14. A can do a piece of work in 9 days. B is 50% more efficient them A. The number of days it takes for B to do the same piece of work is**

(a)13 1/2 days

(b)4 1/2 days

(c) 6 days

(d) 3 days

**15. ‘A can do a piece of work in 25 days and B can do the same work in 30 days. They work together for 5 days and then A leaves. Swill finish the remaining work in **

(a) 11 days

(b) 19 days

(c) 20 days

(d) 21 days

**16. A and B can complete a piece of work in 16 days. A alone can do it in 24 days. How long will B alone take to complete whole work?**

(a) 8 days

(b) 32 days

(c) 40 days

(d) 48 days

**17. If the work done by a man, a woman and a child be in the ratio of 3 : 2 : 1 and if there be in the factory 20 men, 30 women and 36 children, whose daily wages amount to Rs 234, what will be the wages of 15 men, 21 women and 30 children for 18 weeks? **

(a)Rs 22113

(b)Rs 22000

(c)Rs 19800

(d)Rs 19375

**18. A and B working together could mow a field in 28 days and with the help of C they could have mowed it in 21 days. How long would C take by himself?**

(a) 84 days

(b) 90 days

(c) 72 days

(d) 75 days

**Answer**

**Hints & Solutions**

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