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)