Class 8 Chapter 11 Time and Work

 Access answers to Maths RD Sharma Solutions For Class 8 Chapter 11 Time and Work

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

Solution:

The given details are,

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

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

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

Solution:

The given details are,

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

∴ Rohan can complete painting in 18days.

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:

The given details are,

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 (by taking LCM for 5 and 4 which is 20)

= 9/20

∴ Total work done together is 1/(9/20) = 20/9 = 229 days.

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:

The given details are,

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

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

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:

The given details are,

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

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

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:

The given details are,

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

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

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:

The given details are,

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

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

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:

The given details are,

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

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

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:

The given details are,

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

∴ A, B, C and D together can reap the field in = 1/(5/63) = 63/5 = 1235 days.

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:

The given details are,

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

∴ B alone can polish the floor in = 1/(19/240) = 240/19 = 121219 days