Work and Wages-RRB

Work and Wages

If a person can do a piece of work in ‘n’ days, then in one day, the person will do ‘1/n’work. Conversely, if the person does ‘1/n’ work in one day, the person will require ‘n’days to finish the work.

Ratio:

If A is twice as good a workman as B, then:
Ratio of work done by A and B = 2 : 1.
Ratio of times taken by A and B to finish a work = 1 : 2.

Work is the job assigned or job completed. The rate of work is the speed.

If a person completes a work in n days then he will complete  the part in one day.

Ex- 1 Rama  will do a piece of work in 15 days. What part of work will he do in 3 days.

Ans- Rama  will do a piece of work in 15 days.

Hence in one day Rama can do the work in  \frac{1}{15} th of the work.

In 3 days,  =  \frac{1}{15} * 3 =  \frac{1}{5} th of the work will be done.

Ex-2 If A and B can do a piece of work in x and y days respectively, while working alone, they will together take   \frac{xy}{x + y} days to complete the work.

Ex-3  If A, B  and C can do a piece of work in x, y  and z days respectively, while working alone, they will together take  \frac{xyz}{x + y + z}  days to complete the work.

If A can finish a job in x days and B in y days and A, B and C together in s days then,

C can finish the work alone in =  \frac{sxy}{xy - sz - sx}

B + C can finish in   \frac{xs}{x - s } , A + C  can finish in  \frac{sy}{y - s}    days.

Question 1:

4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?

A. 30

B. 40

C. 50

D. 60

E. None of these

Ans- B(40)

Solution:

Let 1 man’s 1 day’s work = x and 1 woman’s 1 day’s work = y

According to question, 4x + 6y = \frac{1}{8}

and  3x + 7y = \frac{1}{10}

Solving the two equations, we get: x = \frac{11}{400} and y = \frac{1}{400}

Hence 1 woman’s 1 day’s work = \frac{1}{400}

⇒10 women’s 1 day’s work = \frac{1}{400} × 10 = \frac{1}{40}

Hence, 10 women will complete the work in 40 days(Ans)

Question 2:

X can do a piece of work in 40 days. He works at it for 8 days and then Y finished it in 16 days. How long will they together take to complete the work?

A. \frac{30}{3}

B. \frac{40}{3}

C. \frac{45}{3}

D. \frac{50}{3}

E. None of these

Solution:

Ans- B(\frac{40}{3})

X can do a piece of work in 40 days.

Work done by X in 8 days \frac{1}{40} × 8 = \frac{1}{5}

Remaining work = 1 – \frac{1}{5}= \frac{4}{5}

According to question, work is done by Y in 16 days 16 × \frac{5}{4} = 20 days.

Now, X’s 1 day’s work = \frac{1}{40}

and Y’s 1 day’s work = \frac{1}{20}

Hence (X + Y)’s 1 day’s work  =(\frac{1}{40} + \frac{1}{20}) = \frac{3}{40}

Hence, X and Y will together complete the work in \frac{40}{3} days.

Question 3:

A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work in how many days.

A. 4

B. 5

C. 6

D. 7

E. None of these

Solution:

Ans- A (4)

Ratio of rates of working of A and B = 2 : 1

So, ratio of times taken = 1 : 2

B’s 1 day’s work = \frac{1}{12}

Hence, A’s 1 day’s work (2 times of B’s work)= \frac{1}{6}

(A + B)’s 1 day’s work =(\frac{1}{6} + \frac{1}{12}) = \frac{3}{12} = \frac{1}{4}

So, A and B together can finish the work in 4 days

Question 4:

A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:

A. \frac{45}{2}

B. \frac{25}{2}

C. \frac{26}{2}

D. \frac{27}2}

E. None of these

Solution:

Ans- A (\frac{45}2})

Ratio of times taken by A and B = 1 : 3.

The time difference is (3 – 1) 2 days while B take 3 days and A takes 1 day.

If difference of time is 2 days, B takes 3 days.

If difference of time is 60 days, B takes =(\frac{3}2}) × 60 = 90 days.

So, A takes 30 days to do the work.

A’s 1 day’s work = \frac{1}{30}

B’s 1 day’s work = \frac{1}{90}

(A + B)’s 1 day’s work = (\frac{1}{30} + \frac{1}{90}) =\frac{4}{90} =\frac{2}{45}

Hence, A and B together can do the work in \frac{45}{2}

Question 5:

A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in how many days?

A. 14

B. 15

C. 25

D. 28

E. None of these

Solution:

Ans- C (25)

(A + B)’s 1 day’s work = \frac{1}{10}

C’s 1 day’s work = \frac{1}{50}

(A + B + C)’s 1 day’s work = (\frac{1}{10} + \frac{1}{50}) = \frac{6}{50} =\frac{3}{25}

A’s 1 day’s work = (B + C)’s 1 day’s work

Hence, 2 x (A’s 1 day’s work) =\frac{3}{25}

⇒A’s 1 day’s work = \frac{3}{50}

Hence B’s 1 day’s work = (\frac{1}{10}) – (\frac{3}{50}) =\frac{(5-3)}{50} = \frac{2}{50} = \frac{1}{25}

So, B alone could do the work in 25 days.

Question 6:

A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is ?

A. \frac{3}{14}

B. \frac{8}{15}

C. \frac{6}{25}

D. \frac{5}{28}

E. None of these

Ans. B(\frac{8}{15})

Solution:

A’s 1 day’s work = \frac{1}{15}

B’s 1 day’s work = \frac{1}{20}

(A + B)’s 1 day’s work = (\frac{1}{15} + \frac{1}{20}) = \frac{7}{60}

(A + B)’s 4 day’s work = 4 × \frac{7}{60} = \frac{7}{15}

Therefore, Remaining work = 1 – \frac{7}{15} =\frac{8}{15}

Question 7:

If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be?

A. 4

B. 5

C. 6

D. 7

E. None of these

Ans-A(4)

Solution:

Let 1 man’s 1 day’s work = x and 1 boy’s 1 day’s work = y.

Then, 6x + 8y = \frac{1}{10}

and 26x + 48y = \frac{1}{2}

Solving these two equations, we get : x = \frac{1}{100} and y = \frac{2}{100}

(15 men + 20 boy)’s 1 day’s work = (\frac{15}{100} + \frac{20}{200}) = \frac{50}{200} =\frac{1}{4}

Hence, 15 men and 20 boys can do the work in 4 days.

Question 8:

10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?

A. 3

B. 5

C. 7

D. 8

E. None of these

Ans-C(7)

Solution:

1 woman’s 1 day’s work = \frac{1}{70}

1 child’s 1 day’s work = \frac{1}{140}

(5 women + 10 children)’s day’s work = (\frac{5}{70} + \frac{10}{140})

=\frac{20}{140} =\frac{1}{7}

Hence, 5 women and 10 children will complete the work in 7 days

Question 9:

Avoya can do a piece of work in 20 days. Binaya is 25% more efficient than Avoya. The number of days taken by Binaya to do the same piece of work is ?

A. 14

B. 16

C. 18

D. 20

E. None of these

Ans-B(16)

Solution:

Ratio of times taken by Avoya and Binaya = 125 : 100 = 5 : 4.

Suppose Binaya takes x days to do the work.

5 : 4 :: 20 : x

\frac{5}{4} = \frac{20}{x}

⇒ 5x = 80

Hence x = 16

i.e, Binaya takes 16 days to complete the work.

Question 10:

A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B had to leave and A alone completed the remaining work. The whole work was completed in how many days?

A. 6

B. 9

C. 12

D. 15

E. None of these

Ans-C(12)

Solution:

Let total work is 1.

(A + B)’s 1 day’s work = (\frac{1}{15}+ \frac{1}{10}) =\frac{10}{60} = \frac{1}{6}

Work done by A and B in 2 days = 2 × \frac{1}{6} = \frac{1}{3}

Remaining work = 1 – \frac{1}{3} = \frac{2}{3}

Now \frac{1}{15}th  work is done by A in 1 day.

Hence \frac{2}{3} work will be done by A in (\frac{2}{3})× 15 = 10 days.

Hence, the total time taken = (10 + 2) = 12 days.