Numerical Ability - Time and Work sample questions with explanation

TIME AND WORK

In solving Time and Work problems the following points need to be remembered

➠ When more men work, they take less time to complete the work.

Similarly when less men work, they take more time to complete the work.

➠ When more men are there, they do more work and less men are there, they do less work.

➠ When men work for more time then they do more work and less time then the work is also less.

➠ If a man can do a piece of work in 'n' days, then his one day's work is 1/n

➠ If a man’s one day’s work is 1/n, then he can complete the entire work in 'n' days.

➠ If a man can do a piece of work in 'A' days and another man can do the same work in 'B' days, then they together can complete the  work in AB/A+B days.

Similarly, three persons A, B and C together can complete in ABC /(AB+BC+AC ) days .

Ex:A can complete a piece of work in 24 days and B in 36 days. In what time they complete if they work together?

A) 18 days B) 30 days C) 7.2 days D) 14.4 days E) 16 days

Sol:         A in 24 days and B in 36 days

if they work together they finish in

AB/(A+B) ⇒  (24 × 36)/(24+36) =14.4 days

MAN DAYS:

➠ If 'm' men can complete a work in 'n' days, then the number of man days required to complete that work is m × n.

For Example: If 6 men can complete a work in 4 days, then the number of man days required to complete that work is 6 × 4 = 24.

Ex: 12 men together can complete a work in 18 days. In how many days 27 men finish that work?

      A)    5 days B) 6 days  C) 10 days D) 8 days E) None of these

Sol:  12 men complete in 18 days. 27 men take less time to complete that work

∴ (12 × 18) / 27 = 8 days.

Shortcut: The work which 12 men finish in 18 days will be finished by 27 men in 'x' days

∴ 12 × 18 = 27 × x

12 × 18

⇒ x = 12 x 18 / 27= 8 days.

➠ M1 persons can do W1 work in time D1 and M2 persons do W2 work in time D2 , then the relation between these quantities is  

M1× D1/W1=M2× D2/W2

Ex: If 10 persons can complete( 2 /5)^th  of the work in 8 days then how many persons required to  complete the remaining work in 12 days?

A) 8 B) 10 C) 6 D) 12 E) None of these

Sol:        M1× D1/W1=M2× D2/W2

here, M1=10, D1= 8, W1= 2/5

M2= ?, D2= 12, W2=3/5

⇒ (10 x 8)/(2/5)=(M2 x 12)/(3/5)

⇒ M2 = (10 x 8 x 3 x5 )/2 x 5 x 10 = 10.

PIPES AND CISTERNS:

The problems in Pipes and Cisterns are similar to those of Time and Work problems, and  negative work will be there due to leakage or drain pipes in the questions.

Ex-1: A pipe fills a tank in 8 hours and a leak in the bottom empties it in 12 hours. In what time can the tank be filled when both function simultaneously?

Pipe's one hour's work = 1/8

Leak's one hour's work = −1/12 (negative work) Pipe and leak together one hour's

 work = 1/8 −1/12 =1/24

Network is positive. Thus tank will be filled in 24 hours

Ex-2: If a pipe fills a tank in 10 hours and a leak empties in 8 hours, when both function simultaneously then in what time can the tank be emptied?

Pipe's one hour's work = 1/10

Leak's one hour's work = − 1/8 (negative work)

Pipe and leak together one hour's work

= (1/10) –(1/8) = −1/40 Network is negative. Thus tank will be emptied in 40 hours.

Some More Models:

1. Raju can do a piece of work in 20 days. Raju and Raghu together can complete the same work in 12 days. In what time does Raghu alone complete that work?

A) 15 days  B) 25 days C) 16 days  D) 30 days E) 28 days

Sol:        Raju and Raghu together's one day's work = 1/12

Raju's one day's work = 1/20

Raghu's one day's work= (1/12)-(1/20)= 1/30

∴ Raghu can complete the work in 30 days.

Shortcut:

 When two persons (x and y) together working time and one of the persons working time is given, then other person's working time is

XY/X-Y ⇒ 20 x 12/(20-12)= 30 days.

2.Abhi and Bhanu can do a piece of work in 24 days. Bhanu and Chandu in 30 days and Chandu and Abhi in 40 days. In what time can Abhi alone do that work?

A) 15 days B) 25 days C) 16 days D) 60 days E) 28 days

Sol:        One day's work of Abhi & Bhanu =1/24

One day's work of Bhanu & Chandu = 1/30

One day's work of Chandu & Abhi = 1/40

Two day's work of Abhi, Bhanu & Chandu

=1/24+1/30+1/40=12/120=1/10

One day's work of Abhi, Bhanu & Chandu = 1/20

One day's work of Abhi  = 1/20-1/30=1/60

∴ Abhi can do that work in 60 days.

3. Shiva can do a work in 20 days. He worked alone for 10 days and the remaining work was completed with the help of Syam in 2 days. In how many days will the total work be completed if they work together?

A) 5 days B) 2.5 days C) 4 days D) 3 days E) 8 days

Sol:        Work of Shiva for 10 days = 1/20 x 10=1/2

 Remaining work = 1-1/2 =1/2

½ the work is done by (Shiva + Syam) = 2 days

∴ Total work is done by (Shiva + Syam) = 2 × 2 = 4 days

4. 12 men can do a piece of work in 18 days. 4 days after they started the work, 8 more men joined  them. How many days will they now take to complete the remaining work?

A) 8.4 days B) 10 days C) 15 days D) 9.4 days E) None of these

Sol:        Total man days required for the work = 12 × 18 = 216

Number of man days completed in 4 days = 4 × 12 = 48

Remaining man days = 216 − 48 = 168

Number of men available now = 12 + 8 = 20

∴ Number of days required =168/20= 8.4

5. Two pipes A and B can fill a tank in 4 and 5 hours respectively. A drain pipe C can empty a full tank in 8 hours. In what time can the tank be filled when all the three are open simultaneously?

A)12 ½ B) 13 1/3     C) 14 ½   D) 14 ½ E) None of these

Sol:        A = 4 hours (+), B = 5 hours (+), C = 8 hours (−)

Three together can fill in ABC/AB+ BC+ CA hours

ð  4 x 5 x (-8)/(20-40-32)

ð  -160/-52 => 13 1/3 hours

EXERCISE

1.A tap can fill a cistern in 8 minutes and another can fill it in 12 minutes. If both are opened simultaneously, find the time that the cistern will be full.

A) 10 min B) 9.6 min C) 12 min D) 7.5 min E) None of these

2. A tap can fill a tank in 15 minutes and another can empty it in 25 minutes. If both are opened simultaneously, in how many minutes the tank is filled?

A) 25 min B) 20 min C) 45 min D) 37.5 min E) 24 min

3.A pipe can fill 80% of the cistern in 24 minutes. In how many minutes it can fill half of the cistern?

A) 16 min B) 15 min C) 12 min D) 20 min E) 18 min

4.A can reap a field in 12 days while A and B together can reap the same field in 4 days. In how many days will B alone can reap that field?

A) 6 B) 8 C) 15 D) 12 E) None of these

5. 15 men can do a piece of work in 28 days. In how many days can 42 men do that work?

A) 36 B) 10 C) 12 D) 24 E) None of these

6.A can finish a piece of work in 5 days and B can do it in 10 days. They work together for two days and then A leaves. In how many days will B finish the work?

A) 6 days B) 8 days C) 12 days D) 4 days E) None of these

7. Shivaram can build a wall in 12 days, Abhiram in 15 days and Parushuram in 18 days. In how many will the wall be built if all the three work together?

A) 4 25/37 days B) 3 32/37 days C) 4 32/33 days D) 4 32/37 days E) None of these

8. A is twice as good a workman as B. If they together can complete a job in 12 days, in how many days B alone can finish that job?

A) 18 days B) 24 days C) 36 days D) 12 days E) None of these

9. In a garrison, provision is sufficient for 250 soldiers for 9 days. But after 3 days 50 more soldiers joined the garrison. For how many days more the provision last for them?

A) 10 days B) 8 days C) 12 days D) 7 days E) None of these

10. 15 men can reap 12 acres working 8 hours a day. How many men are required to reap 18 acres working 6 hours a day?

A) 20 B) 30 C) 50 D) 25 E) 45

Answers

1-E 2-D 3-B 4-A 5-B 6-D 7-D 8-C 9-E 10-C