**Question 1. Rakesh can do a piece of work in 20 days. How much work can he do in 4 days?**

**Solution:**

Given:Time taken by Rakesh to do a piece of work is 20 days

Work done by Rakesh in 1 day = 1/20

Work done by Rakesh in 4 days = 4 × 1/20

= 1/5

Therefore,

1/5th work can be done by Rakesh in 4days.

**Question 2. Rohan can paint 1/3 of a painting in 6 days. How many days will he take to complete painting?**

**Solution:**

Given:Number of days taken by Rohan for painting 1/3 of painting is 6 days

Number of days taken by Rohan to complete the painting = 6/(1/3)

= 6 × 3 = 18

Therefore,

Rohan can complete painting in 18days.

**Question 3. Anil can do a piece of work in 5 days and Ankur in 4 days. How long will they take do the same work, if they work together?**

**Solution:**

Given:Anil can do a piece of work in 5 days

Work done by Anil in 1 day = 1/5

Ankur can do same work in 4 days

Work done by Ankur in 1 day = 1/4

Work done by both in 1 day = 1/5 + 1/4

= (5+4)/20 {taking LCM for 5 and 4 which is 20}

= 9/20

Therefore,

Total work done together is 1/(9/20) = 20/9 = 2

2days.

9

**Question 4. Mohan takes 9 hours to mow a large lawn. He and Sohan together can mow in 4 hours. How long will Sohan take to mow the lawn if he works alone?**

**Solution:**

Given:Mohan can mow a lawn in 9 hours.

Work done by Mohan in 1 hour = 1/9

Mohan and Sohan can mow the lawn together in = 4 hours

Work done by Mohan and Sohan together in 1 hour = 1/4

We know that,

Work done by Sohan in 1 hour = (work done by together in 1 hour) – (work done by Mohan in 1 hr)

= 1/4 – 1/9

= (9-4)/36 {by taking LCM for 4 and 9 which is 36}

= 5/36

Therefore,

Time taken by Sohan to complete the work = 1/(5/36) = 36/5hours.

**Question 5. Sita can finish typing a 100-page document in 9 hours, Mita in 6 hours and Rita in 12 hours. How long will they take to type a 100-page document if they work together?**

**Solution:**

Given:Work done by Sita in 1 hour = 1/9

Work done by Mita in 1 hour = 1/6

Work done by Rita in 1 hour = 1/12

Work done by Sita, Mita and Rita together in 1 hour = 1/9 + 1/6 + 1/12

= (4+6+3)/36 {by taking LCM for 9, 6 and 12 which is 36}

= 13/36

Therefore,

Time taken by all three together to complete the work = 1/(13/36) = 36/13 hours.

**Question 6. A, B and C working together can do a piece of work in 8 hours. A alone can do it in 20 hours and B alone can do it in 24 hours. In how many hours will C alone do the same work?**

**Solution:**

Given:A can do a piece of work in 20 hours

Work done by A in 1 hour = 1/20

B can do same work in = 24 hours

Work done by B in 1 hour = 1/24

A, B and C working together can do the same work in = 8 hours

Work done by A, B, C together in 1 hour = 1/8

We know that,

Work done by C in 1 hour = (work done by A,B and C in 1 hour) – ( work done by A And B in 1 hr.)

= 1/8 – (1/20 + 1/24)

= 1/8 – 11/120

= (15-11)/120 {by taking LCM for 8 and 120 which is 120}

= 4/120

= 1/30

Therefore,

Time taken by C alone to complete the work = 1/(1/30) = 30hours.

**Question 7. A and B can do a piece of work in 18 days; B and C in 24 days and A and C in 36 days. In what time can they do it, all working together?**

**Solution:**

Given:A and B can do a piece of work in = 18 days

Work done by A and B in 1 day = 1/18

B and C can do a piece of work in = 24 days

Work done by B and C in 1 day = 1/24

A and C can do a piece of work in = 36 days

Work done by A and C in 1 day = 1/36

By adding A, B and C we get,

2(A + B + C) one day work = 1/18 + 1/24 + 1/36

= (4 + 3 + 2)/72 {by taking LCM for 18, 24 and 36 which is 72}

= 9/72

= 1/8

A + B + C one day work = 1/(8 × 2) = 1/16

Therefore,

A, B and C together can finish the work in = 1/(1/16) = 16days.

**Question 8. A and B can do a piece of work in 12 days; B and C in 15 days; C and A in 20 days. How much time will A alone take to finish the work?**

**Solution:**

Given:A and B can do a piece of work in = 12 days

Work done by A and B in 1 day = 1/12

B and C can do a piece of work in = 15 days

Work done by B and C in 1 day = 1/15

A and C can do a piece of work in = 20 days

Work done by A and C in 1 day = 1/20

By adding A, B and C we get,

2(A+B+C)’s one day work = 1/12 + 1/15 + 1/20

= (5+4+3)/60 (by taking LCM for 12, 15 and 20 which is 60)

= 12/60

= 1/5

A+B+C one day work = 1/(5×2) = 1/10

We know that,

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

= 1/10 – 1/15

= (3 – 2)/30 (by taking LCM for 10 and 15 which is 30)

= 1/30

Therefore,

A alone can finish the work in = 1/(1/30) = 30days.

**Question 9. A, B and C can reap a field in 15 ¾ days; B, C and D in 14 days; C, D and A in 18 days; D, A and B in 21 days. In what time can A, B, C and D together reap it?**

**Solution:**

Given:A, B and C can reap the field in = 15 ¾ days = 63/4 days

(A, B and C)’s 1 day work =1/(63/4) = 4/63

B, C and D can reap the field in = 14 days

B, C and D’s 1 day work = 1/14

C, D and A can reap the field in = 18 days

C, D and A’s 1 day work = 1/18

D, A and B can reap the field in = 21 days

D, A and B’s 1 day work = 1/21

Now adding (A+B+C+D),

3[A+B+C+D] = 4/63 + 1/14 + 1/18 + 1/21

= (8+9+7+6)/126

= 30/126

= 5/21

(A+B+C+D) = 5/(21×3) = 5/63

Therefore,

A, B, C and D together can reap the field in = 1/(5/63) = 63/5 = 12

3days.

5

**Question 10. A and B can polish the floors of a building in 10 days. A alone can do ¼th of it in 12 days. In how many days can B alone polish the floor?**

**Solution:**

Given:A and B can polish a building in = 10 days

Work done by A and B in one day = 1/10

A alone can do 1/4th of work in = 12 days

A’s 1 day work = 1/(4×12) = 1/48

We know that,

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

= 1/10 – 1/48

= (48-10)/480 {by taking LCM for 10 and 48 which is 480}

= 38/480

= 19/240

Therefore,

B alone can polish the floor in = 1/(19/240) = 240/19 = 12

12days.

19

**Question 11. A and B can finish a work in 20 days. A alone can do 1/5th of the work in 12 days. In how many days can B alone do it?**

**Solution:**

Given:A and B can finish a work in = 20 days

(A+ B)’s 1 day work = 1/20

A can finish 1/5th of work in = 12 days

A’s 1 day work = 1/(5 × 12) = 1/60

We know that,

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

= 1/20 – 1/60

= (3 – 1)/60

= 2/60

= 1/30

Therefore,

B alone can finish the work in = 1/(1/30) = 30days.

**Question 12. A and B can do a piece of work in 20 days and B in 15 days. They work together for 2 days and then A goes away. In how many days will B finish the remaining work?**

**Solution:**

Given:A and B can do a piece of work in = 20 days

Work done by A and B in 1 day = 1/20

B can do a piece of work in = 15 days

B’s 1 day work = 1/15

A and B work for 2 days, hence work done by them in 2 days = 2 × 1/20 = 1/10

Remaining work = 1 – 1/10 = 9/10

Therefore,

B can finish the remaining (9/10) work in = (9/10)/15 = 135/10 = 13 ½ days.

**Question 13. A can do a piece of work in 40 days and B in 45 days. They work together for 10 days and then B goes away. In how many days will A finish the remaining work?**

**Solution:**

Given:A can do a piece of work in = 40 days

A’s 1 day work = 1/40

B can do a piece of work in = 45 days

B’s 1 day work = 1/45

(A+B)’s 1 day work together = 1/40 + 1/45

A+B’s 10 day work together = 10 (1/40 + 1/45)

= 10 ((9+8)/360) (by taking LCM for 40 and 45 which is 360)

= 10 × 17/360

= 17/36

Remaining work = 1 – 17/36

= (36 – 17)/36

= 19/36

Therefore,

A can finish the remaining (19/36) work in = (19/36)/(1/40)

= (19/36) × 40

= 190/9

= 21

1days.

9

**Question 14. Aasheesh can paint his doll in 20 minutes and his sister Chinki can do so in 25 minutes. They paint the doll together for five minutes. At this juncture, they have a quarrel and Chinki withdraws from painting. In how many minutes will Aasheesh finish the painting of the remaining doll?**

**Solution:**

Given:Aasheesh can paint his doll in = 20 minutes

Aasheesh can paint his doll in 1 minute = 1/20

Chinki can paint the same doll in = 25 minutes

Chinki can paint the same doll in 1 minute = 1/25

Together they both can paint the doll in 1 minute = 1/20 + 1/25

= (5+4)/100 {by taking LCM for 20 and 25 which is 100}

= 9/100

Work done by them in 5 minute = 5 × 9/100

= 9/20

Remaining work = 1 – 9/20

= (20-9)/20

= 11/20

Therefore,

Aasheesh can paint the remaining doll in = (11/20)/(1/20)

= 11/20 × 20

= 11 minutes