# Examples of Time and work

In the earlier article, you have learnt important formulas which are used to solve questions of Time and Work. Using them and some common sense and logic, we’ll learn how to solve questions of Time and Work. Read on.

## Solve examples given below and choose appropriate option as an answer.

Examples of Time and Work

1. Rahul completes a certain work in 15 days while Piyush takes 10 days to complete the same. In how many days would they complete the work if they work together ?

(A) 9 days (B) 6 days (C) 12 days (D) 8 days

Solution:

Rahul’s daily work = 1/15 ( S = W / T )

Piyush’s daily work = 1/10

If they work together,

Speed of work

= 1/15 + 1/10

= 5/30

= 1/6

So, working together, they would take 6 days to complete the work.

That is (B)

Note : We are giving here explanations for your understanding. When in exam, you should use direct calculations with minimum use of words so that you can attend a question in given time. In future, we may teach you shortcuts for faster calculation, but for now, clear the concept in your mind. Also, some complex calculations are published using LaTeX markup language and so their fonts may be somewhat different than normal text and numbers. Hope, you will understand that. Keep learning.

2. X person can finish a work in 12 days when working for 5 hours a day while Y person can finish the same work in 10 days when working for 8 hours a day. To finish the work faster, they both work together for 12 hours a day. Approximately, in how many days the work would be completed?

(A) 3 days (B) 5 days (C) 4 days (D) 2 days

Solution:

We need to find the speed in hours here,

X works for 12 x 5 = 60 hours

∴ His speed = 1/60

Y works for 10 x 8 = 80 hours

∴ His speed = 1/80

Together,

Speed = 1/60 + 1/80

= 7 / 240 in 1 hour

So, working together, they would complete the work in 240/7 hours.

They work for 12 hours a day,

$\frac { 240/7 }{ 12 } =\frac { 20 }{ 7 } =2\frac { 6 }{ 7 } \cong 3$

So, they would complete the work in 3 days.

That is (A)

3. I can complete a certain work in 24 months and you can complete the same work in 18 months. We both start working together and after 6 months, I have to leave the work. In how many months, you would complete the remaining work ?

(A) 6.5 months (B) 5 months (C) 7.5 months (D) 6 months

Solution:

My Speed = 1/24

Speeds here are in months,

Working together,

Speed = 1/24 + 1/18

= 7/72

Now, we work together for 6 months, so,

$6\times \frac { 7 }{ 72 } =\frac { 7 }{ 12 }$ work is done.

Remaining work = 1 – 7/12

= 5/12

You would complete that in,

$\frac { 5/12 }{ 1/18 } =\frac { 15 }{ 2 }=7.5$

7.5 months.

That is (C)

4. A can complete a work in 10 days. B can complete that in 15 days and C can complete that in 20 days. If they work together, in how many days the work would be completed ?

(A) 8 days (B) 5 days (C) 4 8/13 days (D) 6 days

Solution:

While working together,

Their speed,

= 1/10 + 1/15 + 1/20

= 13/60

They would complete the work in,

$\frac { 60 }{ 13 } =4\frac { 8 }{ 13 } days$

That is (C)

5. A can complete a work in 10 days. B can complete that in 15 days and C can complete that in 20 days. All of them work together for 2 days and then A and C left. In how many days, the remaining work would be completed by B ?

(A) 8 days (B) 8.5 days (C) 7.5 days (D) 6 days

Solution:

( A + B + C )’s work in 1 day,

= 1/10 + 1/15 + 1/20

= 13/60

They work for 2 days,

so, 2 x 13/60 = 26/60 = 13/30 work is done.

Remaining work = 1 – 13/30

= 17/30

Which is to be completed by B,

$=\frac { 17/30 }{ 1/15 }$ ( T = W / S )

= 17 x 15 / 30

= 8.5 days

So, the remaining work would be completed in 8.5 days by B.

That is (B)

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6. X can finish a work in 10 days and Y can finish that in 15 days. They both work together for 3 days and then leave the work. How much work is left to be done ?

(A) 1 / 2 (B) 1 / 4 (C) 2 / 3 (D) 3 / 4

Solution:

Working together,

Daily Speed,

= 1 / 10 + 1 / 15

= 1 / 6

They work for 3 days,

So,

3 x 1 / 6 = 3 / 6 = 1 / 2 work is done.

So, 1 – 1 / 2 = 1 / 2 work is left to be done.

That is (A)

7. A can complete a piece of work in 5 days, B and C can complete that in 8 and 20 days respectively. A and B work together for 2 days and then left the work for C to complete. In how many days would C complete that ?

(A) 6 days (B) 7 days (C) 3 days (D) 8 days

Solution:

Speed of A = 1 / 5, B = 1 / 8 and C = 1 / 20

( A + B )’s Speed

= 1 / 5 + 1 / 8

= 13 / 40

They work for 2 days,

∴ 2 x 13 / 40

= 26 / 40

= 13 / 20 work is done.

Remaining work

= 1 – 13 / 20

= 7 / 20

That is to be done by C,

So, the time taken by him

$=\frac { 7/20 }{ 1/20 }$

= 7 days

That is (B)

8. A certain work is completed in 20 days by Sameer and in 30 days by Rajesh if they work individually. In how many days 75% work would be completed by them while they work together?

(A) 10 days (B) 12 days (C) 9 days (D) 15 days

Solution:

A’s speed = 1 / 2

B’s speed = 1 / 30

When they work together, Speed,

= 1 / 20 + 1 / 30

= 5 / 60

= 1 / 12

Now,

75 % = 75 / 100 = 3 / 4 work is to be done.

So, they would take,

$=\frac { 3/4 }{ 1/12 }$

= 9 days

That is (C)

9. There is a work which can be completed by Ramesh in 20 days while Suresh takes double the time. They both start working together and after 6 days, Ramesh leave the work and the remaining work is to be completed by Suresh. How many days will he take to complete the work ?

(A) 11 days (B) 12 days (C) 30 days (D) 22 days

Solution:

Ramesh’s speed = 1 / 20

Suresh’s speed = 1 / 40 ( Suresh takes double time i.e. 40 days )

Together, Speed

= 1 / 20 + 1 / 40

= 3 / 40

They work together for 6 days,

$\therefore6\times \frac { 3 }{ 40 } =\frac { 18 }{ 40 } =\frac { 9 }{ 20 }$

∴ Work done = 9 / 20

Remaining work = 1 – 9 / 20 = 11 / 20

Suresh has to complete that,

So, Time taken by him

$=\frac { 11/20 }{ 1/40 } =\frac { 440 }{ 20 } =22$

So, Suresh would take 22 days to complete the work.

That is (D)

10. A certain piece of work is done by Sachin, Saurav and Rahul in 35 hours, 60 hours and 50 hours respectively. If they work together, in how many hours the work would be completed ?

(A) 15 45/137 hours (B) 20 hours (C) 13 43/137 hours (D) 20 45/137 hours

Solution:

When they work together, Speed,

= 1 / 35 + 1 / 60 + 1 / 50

$=\frac { 60+35+42 }{ 2100 }$ ( LCM of 35,60 and 50 is 2100)

= 137 / 2100

So, the work would be completed in,

= 2100 / 137

$=15\frac { 45 }{ 137 } hours$

That is (A)

11. In the example 9, if 10,000 Rs. are paid to Ramesh and Suresh for total work, how much each one of them should get ?

(A) Ramesh 3000 Rs., Suresh 7000 Rs. (B) Ramesh 4000 Rs., Suresh 6000 Rs.

(C) Ramesh 3500 Rs., Suresh 6500 Rs. (D) Ramesh 7000 Rs., Suresh 3000 Rs.

Solution:

Ramesh works for 6 days, so,

= 6 x 1 / 20

= 6 / 20

= 3 / 10 work is done by him.

Remaining work,

= 1 – 3 / 10

= 7 / 10 work is done by Suresh.

So, Ramesh gets 3 / 10 x 10000 = 3000 Rs.

And Suresh gets 7 / 10 x 10000 = 7000 Rs.

That is (A)

12. A can finish a work in 14 days while B can finish that in 21 days. If they work together, in how many days the work would be completed? If they are paid 8000 Rs. for the work, how much each one of them should get?

(A) 8 3/2days, A 4500 Rs., B 3500 Rs. (B) 8 days, A 3200 Rs., B 4800 Rs.

(C) 8 2/5 days, A 4800 Rs., B 3200 Rs. (D) 12 days, A 4600 Rs., B 3400 Rs.

Solution:

Together their speed,

= 1 / 14 + 1 / 21

= 5 /42

So, the work would be completed in,

$\frac { 42 }{ 5 } =\quad 8\frac { 2 }{ 5 } days$

$Work done by A=\frac { 1/14 }{ 42/5 } =\frac { 3 }{ 5 }$

$Work done by B=\frac { 1/21 }{ 42/5 } =\frac { 2 }{ 5 }$

So, A gets, 3 / 5 x 8000 = 4800 Rs.

and B gets, 2 / 5 x 8000 = 3200 Rs.

That is (C)

13. A alone can do a piece of work in 18 days. B alone can do the same work in 12 days. With the help of C, they complete the work in 36/11 days. In how many days, C alone can complete the work?

(A) 10 days (B) 6 days (C) 9 days (D) 11 days

Solution:

Suppose C can complete the work in x days,

Together, they complete the work in 36 / 11 days.

So, ( A+B+C )’s speed = 11 / 36

$\therefore \frac { 1 }{ 18 } +\frac { 1 }{ 12 } +\frac { 1 }{ x } =\frac { 11 }{ 36 }$

$\frac { 1 }{ x } =\frac { 11 }{ 36 } -\frac { 1 }{ 18 } -\frac { 1 }{ 12 }$

$\frac { 1 }{ x } =\frac { 11-2-3 }{ 36 }$

$\frac { 1 }{ x } =\frac { 6 }{ 36 }$

∴ x = 6

so, C alone can complete the work in 6 days.

That is (B)

14. Vishal is thrice as good worker as Vivek. While working together, they complete a certain work in 6 days. In how many days, Vishal alone can complete the work ?

(A) 8 days (B) 16 days (C) 9 days (D) 12 days

Solution:

Suppose, Vishal takes x days for the work,

So, Vivek would take 3x days. ( Vivek being thrice slower takes thrice the time )

Working together, they complete a work in 6 days,

$\therefore6(\frac { 1 }{ x } +\frac { 1 }{ 3x } )=1$

$6(\frac { 3+1 }{ 3x } )=1$

$\frac { 24 }{ 3x } =1$

x = 8

So, Vishal alone can complete the work in 8 days.

That is (A)

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15. 10 boys and 12 girls can complete a piece of work in 20 days while 15 boys and 28 girls can complete the same work in 10 days. In how many days 20 boys and 64 girls would complete the same work ?

(A) 6 days (B) 10 days (C) 9 days (D) 5 days

Solution:

Suppose a boy’s daily work = x and a girl’s daily work = y

∴10 x + 12 y = 1 / 20

15 x + 28 y = 1 / 10

Solving these equations, we get,

x = 1 / 500 and y = 1 / 400

Now, 20 boys’ and 64 girl’s daily work,

= 20 ( 1 / 500 ) + 64 ( 1 / 400 )

= 1 / 25 + 4 / 25

= 5 / 25

= 1 / 5

So, they would complete the work in 5 days.

That is (D)

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