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In this article, we will delve into the solutions for Exercise 11.1 Set 1 from Chapter 11 of RD Sharma's Class 8 Mathematics textbook which focuses on "Time and Work". This chapter is fundamental for understanding how to manage and calculate work done over time a concept applicable in various real-life scenarios. The solutions provided here aim to clarify the methods and techniques used to solve problems related to time and work.
The concept of "Time and Work" deals with determining how long it takes for one or more individuals to complete a task and how their combined efforts affect the time required. It involves calculating the amount of work done in the given time frame and finding the time required to complete a task based on the rate of work. Understanding these principles helps in solving problems related to efficiency, productivity, and resource management.
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.
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.
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 days.
9
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.
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.
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.
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.
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.
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 days.
5
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 days.
19
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.
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.
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 days.
9
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
Read More:
Chapter 11 of RD Sharma Class 8 focuses on Time and Work problems. This chapter deals with calculating the relationship between the number of workers, time taken, and work done. It teaches students how to solve problems involving direct and inverse variations in the context of time and work scenarios. The chapter covers concepts such as work done by multiple workers, time taken to complete tasks, and efficiency in completing jobs.
