## Time and Work for RRB JE

Every single mark scored in the RRB JE exam can bring a big change in the result of individual aspirants. Therefore, every topic listed in the RRB JE syllabus should be thoroughly prepared. But among so many topics, Time and Work are one of the topics for the RRB JE exam in which candidates can easily score good marks.

## Important Time and Work Formula

While solving time and works problems candidates can make use of the following list of formulas. These are the most important and commonly used in solving RRB JE time and work questions:

- Work Done = Total Time Taken multiplied by the rate of work.
- Whereas the Rate of Work is equal to 1/Time Taken.
- Time taken is equal to 1 divided by the rate of work.

## Time and Work Questions for RRB JE Exam

Time and work are considered to be easy. However, it requires a little effort to learn the concepts of time and work and with practice, candidates can master Time and Work for RRB JE. Here are some time and work questions for the RRB JE exam. Aspirants can solve it to get an overview of the Time and Work questions that usually come in the RRB JE exam.

1. A alone can do a piece of work in 60 days and B alone can do the same work in 75 days. If A and B worked on alternate days, and first A started the work, then in how many days the work will be completed?

A. 66 & 3/5 days

B. 64 days

C. 65 & 3/5 days

D. 64 & 2/5 days

E. None of these.

Answer : A

Solution :

Let total work = LCM of 60 and 75 = 300 units

One day work of A =300/60 = 5 units.

One day work of B =300/75 = 4 units.

First two days work of A and B = 5 + 4 = 9 units.

The number of two days pair = 300/ 9 = 33 pair

First 66 days work of A and B =33 x 9 =297 units.

Remaining = 300 -297 = 3 units.

67th day A worked, so time taken by A to complete 3 units = 3/5 days.

Total days =66 & 3/5 days.

2. Rs 7.25 and Rs 6 are alloted as Daily wage for A and B respectively. A can complete the work in 8 days and B can complete the work in 9 days. If both of them work together then what will be the cost of the work?

A. Rs.54

B. Rs.58

C. Rs.562/17

D. Rs.491/9

E. Rs.61.75

Answer : C

Solution :

A can complete the work in 8 days.

B can complete the work in 9 days.

Let the total work = 72 ( because 72 is the L.C.M. of 8 and 9 )

One day work of A = 72/8 = 9

One day work of B =72/9 = 8

A and B start working together.

Time taken to complete the work when A and B work together =72/(9+8) = 72/17

Rs 7.25 and Rs 6 are alloted as Daily wage for A and B respectively.

Sum of daily wage of A and B = 7.25 + 6 = 13.25 or Rs. 53/4

Total Cost of the work = (72/17) X (53/4) =954/17

= Rs.562/17

3. To complete a work, A takes 45 more days than (A + B) together. While B takes 5 more days than (A + B) together to complete the same work. Then find in how much time (A + B) together will take to complete the work?

A. 5 days

B. 15 days

C. 18 days

D. 24 days

E. 9 days

Answer : B

Solution :

Let the total work = y

Let (A + B) will complete work in “x” days

So, one day work of (A + B) = y/x

According to question---

Time taken by A to complete the work = x + 45

One day work of A = y/(x+45)

Time taken by B to complete the work = x + 5

One day work of B = y / (x+5)

Now, compare the one day work of A and B together and separately---

y/x = y/(x+45) + y/ (x+5)

1/x = 1/(x+45) + 1/(x+5)

1/x = (2x + 50 ) / ( x2+50x+225)

x2+50x+225 = 2x2 + 50

x = 15 days

Hence, (A+B) together will take 15 days to complete the work.

4. A alone can complete a piece of work in 12 days and B alone can complete the same piece of work in 20 days. If B started the work and A and B worked on alternate days, then in how many days the work will be completed?

A. 7 & 4/5

B. 16 & 2/3

C. 18 & 1/2

D. 15 & 1/5

E. None of these

Answer : D

Solution :

Let total work be 60 unit(L.C.M of 12, 20)

Efficiency of A = 60 ÷ 12 = 5 unit/day

Efficiency of B = 60 ÷ 20 = 3 unit/day

Amount of work done in 2 days = 3 + 5 = 8 units

So, time taken to complete the work = () days

= 14 + 1 + 1/5

=15 & 1/5

5. 20 men, 12 women and 18 boys were given a task of digging 1980m canal in 5 days. The ratio of the work done by a man, a woman and a boy respectively in 1 day is 3 : 2 : 1. If on the 1st day all of them worked, on the 2nd day 4 women and 6 boys were absent and on the 3rd day, 6 men and 10 boys were absent but still the work was finished on the 3rd day. Then find the length of canal dug by them on the 3rd day (in m).

A. 520

B. 555

C. 820

D. 605

E. None of these

Answer : B

Solution :

Let the distance of canal dug by a man, a woman and a boy in 1 day be 3x, 2x and x respectively.

Distance dug on the 1st day = 20 × 3x + 12 × 2x + 18 × x = 102x

On the 2nd day = 20 × 3x + 8 × 2x + 12 × x = 88x

On the 3rd day = 14 × 3x + 12 × 2x + 8 × x = 74x

Now, 102x + 88x + 74x = 1980

⇒ 264x = 1980 ⇒ x = 7.5

So, Canal dug on the 3rd day = 7.574 =555 m

6. A can complete a certain piece of work in 36 days and B can complete the same work in 24 days. They both worked together along with a third man C and complete the work in 12 days. Then find the time C will take to complete the work alone?

A. 36 days

B. 96 days

C. 48 days

D. 72 days

E. 24 days

Answer : D

Solution :

A can complete a work in 36 days.

B can complete the same work in 24 days.

Let the Total work = 72 units ( because 72 is the L.C.M. of 36 and 24 )

One day work of A = 72/36 = 2 units

One day work of B = 72/24 = 3 units

A and B worked with a third man C and complete the work in 12 days.

One day Work of (A + B + C) = 72/12 = 6 units

Now we can calculate on day work of C.

One day work of C = 6 – (2 + 3) = 1 units

Time taken by C alone to complete the work = 72/1

= 72 days

Hence, C can complete the work alone in 72 days.

7. A man takes 1 day less than the time taken by a woman to finish a piece of work. If both man and woman together can finish it in 10 days, then how many days a woman will take to finish the work alone?

A. 0.5

B. 20.5

C. 15

D. 18

E. 24

Answer : B

Solution :

Let woman takes w days to complete the work. So, man takes = (w − 1) days

w(w-1)/(2w-1) = 10

w2-21w+10 = 0

w = 20.51 , 0.48

But 0.48 is not possible

So, woman works for approx. 20.5 days

8. A group of (x – 1) men work for (x + 1) days while another group of (x + 1) men work for (x + 2) days. Ratio of the amount of the total work done by the two groups is 3 : 4. If the efficiencies of all the men are same, then what is the value of x?

A. 8

B. 10

C. 1

D. 11

E. 9

Answer : B

Solution : Let the work done by 1st group and 2nd group of men be W1 and W2 respectively.

According to the question

(x – 1) × (x + 1) = (W1)

(x + 1) × (x + 2) = (W2)

Also, it is given that

w1/w2 = 3/4 = (x-1)(x+1) / (x+1) (x+2)

⇒ 4 × (x – 1) = 3 × (x + 2)

⇒ x = 10

9. A alone can do a piece of work in 6 days. B can do the same piece of work in 8 days. A and B signed to do it for Rs. 3200. They completed the work in 3 days with the help of C. How much is to be paid to C?

A. Rs. 380

B. Rs. 600

C. Rs. 400

D. Rs. 420

E. None of these

Answer : C

Solution : Let the total work = 24 units

Work done by A per day = 24/6 = 4 units

Work done by B per day = 24/8 = 3 units

Work done by (A + B + C) per day = 24/3 = 8 units

Work done by C per day = (8 − 4 − 3) = 1 unit

Ratio of wages of A, B and C = Ratio of their efficiency = 4 : 3 : 1

Amount paid to C =[1/(4+3+1)]3200 = RS. 400

10. Anu, Bhanu and Chandu together can do half of the work in 4 days and Bhanu and Chandu can finish 3/10 part of the work in 4 days. Find in how many days Anu alone can complete the whole work.

A. 10 days

B. 20 days

C. 30 days

D. 40 days

E. None of the above

Answer : B

Solution :

Anu, Bhanu and Chandu together can do half of the work in 4 days, so they do full work in 8 days.

Bhanu + Chandu = 10/3 * 4 = 40/3 days

According to the question,

1/ Anu + 3/40 = 1/8

Therefore, Anu completes the whole work in 20 days.

11. 14 men can complete a work in 10 days. 20 women can complete the same work in 14 days. 10 men and 6 women started working and after 8 days 10 more women join them. How many more days will they take to complete the remaining work.

A. 2 days

B. 2 & 1/2 days

C. 3 days

D. 4 days

E. None of these

Answer : A

Solution : Total work done by 14 men and 20 women is equal

Therefore, efficiency of men and women

14*M*10 = 20* W* 14

M : W = 2 : 1

Total work = 14 * 2 * 10 = 280 unit

Work done by 10 men and 6 women in 8 days = (10* 2 + 6* 1)* 8

= 208 unit

Remaining work = 280 – 208 = 72 unit

Total Efficiency (inclusive of 10 women) = 26 + (10 × 1) = 36

Remaining work done in =72/36 = 2 days

12. Jack is twice efficient as Jill and Jill can do a piece of work in 30 days. Jill started the work and after a few days Jack joined him. They completed the work in 22 days. For how many days they worked together?

A. 6 days

B. 8 days

C. 4 days

D. 10 days

E. None of these

Answer : C

Efficiency of Jill = 1

Efficiency of Jack = 2

Number of Days Jil = 30

Number of Days Jack = 15

Jill’s one day work = 1/30

Jack’s one day work =1/15

(Jack + Jill) one day work =1/30 + 1/15= 1/10

Now, let us assume Jack joined Jill after (22 - X) days then,

(22-X)/30 + (X*1)/10 = 1

(22-X+3X / 30 )= 1

22+2X = 30

X = 4

13. A carbon copier requires 27 bundles of paper for 6 days. How many bundles of paper will be required for 14 days?

A. 43

B. 36

C. 63

D. 44

E. None of these

Answer : C

Solution : For 6 days, number of bundles of papers requires = 27

∴ For 1 days, number of bundles of papers will require = 27/6

∴ For 14 days, number of bundles of papers will require = (27/6)14 = 63

Thus, 63 bundles of papers will be required for 14 days.

Hence, option C is correct.

14. A man, a woman and a boy can do a work in 4, 8, 16 days respectively. How many children were required with 1 man and 1 woman to complete the same work in 1/2 day?

A. 26

B. 32

C. 28

D. 44

E. None of these

Answer : A

Solution : Work done by a man in 1/2days = 1/8 part

Work done by a woman in 1/2 days = 1/16 part

Work done by a boy in 1/2 days = 1/32 part

Let one man and one woman together can do a piece of work in 1/2 days = No. of X children required

According to the question,

1/8 + 1/16 + x/32 = 1

(4+2+X)/32 = 1

6 + x = 32

x = 32-6 = 26

Hence, 26 boys will be required.

15. A is 50% as efficient as B. C does half the work done by A and B together. If C alone does the work in 40 days, then A can do the work in?

A. 50 days

B. 48 days

C. 56 days

D. 60 days

E. None of these

Answer : D

Solution :

Given A is 50% as efficient as B and C’s efficiency is half of (A+B)’s efficiency

Efficiency of A : B = 1 : 2

Efficiency of ( A+B ) : C = 3 : (3/2)

Eff.A X TA = Eff.C X Tc

1 X TA = (3/2) X 40

TA = 60 days

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