TIME AND WORK
SOLVED NUMERICAL PROBLEMS
(PITAMBAR LAL ARITHMETIC )
1. A can do a piece of work in 20 days and B can do it in 30 days ,how long would they take to do it working together ?
Answer:
A 20days 1 work ,
A 1day 1/20 work,
B 30days 1 work,
B 1day 1/3 work,
A+B 1day 1/20 + 1/30 = 5/60 = 1/12 work,
A+B 1/12 work 1day,
A+B 1 work 1/(1/12) = 12 days.
Answer: 12days2. A, B and C can do a piece of work in 6, 12 and 24 days respectively. In what time will they altogether
do it?
Answer:
A 6 days 1 work,
A 1day 1/6 work,
B 12days 1 work,
B 1day 1/12 work,
C 24days 1 work,
C 1day 1/24 work,
A+B+C 1day 1/6 +1/12 +1/24 =7/24 work,
A+B+C 7/24 work 1 day,
A+B+C 1 work 1/(7/24) = 24/7 = 3 3/7 days.
Answer: 33/7 days
3. A and B working together can do a piece of work in 6 days ,B alone can do it in 8 days . Supposing B
works at it for 5 days, In how many it ? days A alone can finish it?
Answer:
A+B 6 days 1 work,
A+B 1day 1/6 work,
B alone 8days 1 work,
B alone 1day 1/8 work,
B alone 5 days 5/8 work,
A alone 1 day 1/6 – 1/8 = 1/24 work,
Remaining work completed by A = 1 – 5/8 = 3/8,
A 1/24 work 1 day,
A 1 work 1/(1/24) day =24 days,
A 3/8 work 24X3/8 = 9 days.
Answer: 9 days.
4. A and B can do a piece of work in 30 days , B and C in 40 days while C and A in 60 days.
How long will they take to finish it together ?
Answer:
A + B 30 days 1 work,
A + B 1 day 1/30 work,
B + C 40 days 1 work ,
B +C 1 day 1/40 work,
C + A 60 days 1 work,
C + A 1 day 1/60 work,
A + B + B + C + C + A 1 day (1/30 + 1/40 + 1/60) work,
2(A + B + C) 1 day 3/40 work,
( A + B + C) 1 day 3/80 work,
(A + B + C) 3/80 work 1 day,
(A + B +C) 1 work 1/(3/80) day = 80/3 = 26 2/3 days.
Answer: 26 2/3 days.
5. A , B and C can reap a field in 15 3 /4 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 A , B , C and D together reap it ? In what time B alone reap it ?
Answer:
A + B + C 15 3 / 4 days reap 1 field,
A + B + C 1 day reap 1/15 3 /4 =1/(63/4) =4/63 field ,
B + C + D 14 days reap 1 field,
B + C + D 1 day reap 1/14 field,
C + D + A 18 days reap 1 field,
C + D + A 1 day reap 1/18 field,
D + A + B 21 days reap 1 field,
D + A + B 1 day reap 1/21 field,
(A +B + C + B + C + D + C + D + A + D + A + B) 1 day reap (4/63 + 1/14 + 1/18 + 1/21) field,
3( A + B + C + D) 1 day reap 5/21 field,
3( A + B + C + D) reap 5/21 field 1 day,
( A + B + C + D) reap 5/21X3 field 1 day,
( A + B + C + D) reap 5/63 field 1day,
( A + B + C + D) reap 1 field 1/(5/63) = 63/5 = 12 3 /5 days.
Answer: 12 3 /5 days.
Now, for the second part of the question,
( A + B + C + D) – ( C + D + A ) 1 day reap (5/63 – 1/18) field,
B alone 1 day 3/126 field,
B alone reap 3/126 field 1 day,
B alone reap 1 field 1/(3/126) = 126/3 = 42 days
. Answer: 42 days.
6. A and B working together could mow a field in 28 days and with the help of C they could have mowed it in 21 days. How long would C take by himself ?
Answer:
A + B 28 days mow 1 field,
A + B 1 day mow 1/28 field,
A + B + C 21 days mow 1 field,
A + B + C 1 day mow 1/21 field,
( A + B + C) – ( A + B) 1 day mow (1/21 – 1/28) field,
C alone 1 day mow 1/84 field,
C alone mow 1/84 field 1 day,
C alone mow 1 field 1/(1/84) = 84 days.
Answer: 84 days.
7. A can copy 75 pages in 25 hours , A and B together can copy 135 pages in 27 hours . In what time B copy 42 pages ?
Answer:
A copy 75 pages 25 hours,
A copy 1 page 25/75 = 1/3 hours,
A copy 1/3 hours 1 page,
A copy 1 hour 1/(1/3) = 3 page,
(A + B) copy 135 pages 27 hours,
(A + B) copy 1 page 27/135 = 1/5 hour,
(A + B ) copy 1/5 hour 1 page,
(A + B) copy 1 hour 1/(1/5) = 5 page,
(A + B) – (A) copy 1 hour (5 – 3) = 2 page,
B copy 2 page 1 hour,
B copy 1 page 1/2 hour,
B copy 42 pages 1/2 X 42 = 21 hours.
Answer: 21 hours.
8. A can do a piece of work in 5 days, B in 4 days, and A, B and C together in 2 days. In what time could C do it alone?
Answer:
A 5 days 1 work,
A 1 day 1/5 work,
B 4 days 1 work,
B 1 day 1/4 work,
A + B 1 day (1/5 + 1/4) = 9/20 work,
(A + B + C) 2 days 1 work,
(A + B + C) 1 day 1/2 work,
(A + B + C) – (A + B) 1 day (1/2 – 9/20) =1/20 work,
C alone 1/20 work 1 day,
C alone 1 work 1/(1/20) = 20 days.
Answer: 20 days.
9. A, B and C can finish a piece of work in 10, 12 and 15 days respectively. If B stops work after 2 days,how long would it take A and C to finish the remaining work ?
Answer:
A 10 days 1 work,
A 1 day 1/10 work,
B 12 days 1 work,
B 1 day 1/12 work,
C 15 days 1 work,
C 1 day 1/15 work,
(A + B + C) 1 day 1/10 + 1/12 + 1/15 = 15/60 = 1/4 work,
(A + B + C) 2days 2X1/4 = 1/2 work,
Remaining work after 2 days = (1 – 1/2) = 1/2 work,
A + C 1 day ( 1/10 + 1/15) = 10/60 = 1/6 work,
A + C 1/6 work 1 day,
A + C 1 work 1/(1/6) = 6 days,
A + C ½ work 6X1/2 = 3 days.
Answer: 3 days.
10. B can do a work in 6 hours, B and C can do it in 4 hours and A, B and C in 2 2 / 3 hours
In how many hours A and B do it?
Answer:
B 6 hours 1 work,
B 1 hour 1/6 work,
B + C 4 hours 1 work,
B + C 1 hour 1/4 work,
( B+ C ) – ( B ) 1 hour ( 1/4—1/6) = 1/12 work,
C 1 hour 1/12 work,
(A + B + C) 8/3 hours 1 work,
(A + B + C) 1 hour 1/(8/3) = 3/8 work,
(A + B + C) – C 1 hour 3/8 – 1/12 = 7/24 work,
A + B 7/24 work 1 hour
A + B 1 work 1/(7/24) = 24/7 = 33/7 hours.
Answer: 33/7 hours.
11. A can finish a piece of work in 15 days of 8 hours, B can finish it in 62/3 days of 9 hours. Find in how many days they can finish it together if they work 10 hours a day.
Answer:
A 15 days of 8 hours 1 work,
A 15 days of 1 hours 1/8 work,
A 1 day of 1 hour 1/(8X15) work ,
B 62/3 days of 9 hours 1 work,
B 62/3 days of 1 hour 1/(20/3) work,
B 1 day of 1 hour 1/(20/3X9) work,
(A+B) 1 day of 1 hour 1/120 +1/60= 1/40 work,
(A+B) 1 day of 10 hours 10X 1/40 =1/4 work
(A+B) 1 work 1/(1/4) days = 4 days
Answer :4 days
12.A can do a piece of work in 62/3 days and B in 5 days. They work together for 2 days ; and then A leaves B to finish the work alone. How long will B take to finish it?
Answer:
A 62/3 days 1 work
A 1 day 1/(62/3 ) work = 3/20 work
B 5 days 1 work
B 1 day 1/5 work
A+B 1 day (3/20 +1/5)= 7/20 work
A+B 1 work 1/(7/20) =20/7 days
But as A leaves after 2 days ,
Work left to be done by B = (6/7 /20/7) = 3/10 work
B 1 work 5 days
B 3/10 work (3/10 X5)= 3/2 days = 1 1/2 days
Answer: 1 1/2 days
13. A and B working separately can do a piece of work in 8 and 10 hours respectively. If they work for an hour alternately, A beginning, in how many hours will the work be completed?
Answer:
A 8 hours 1 work
A 1 hour 1/8 work
B 10 hours 1 work
B 1 hour 1/10 work
If (A+B) work alternately,
(A+B) 2 hours (1/8+ 1/10 ) work =9/40 work
(A+B) 1 hour 9/(40X2) =9/80 work
(A+B) 1 work 1/(9/80)=80/9 hours
But, as A begun the work alternately followed by B, the work has to be ended by A;
Hence work need to be done by A = 8/9/80/9 = 1/10 work (A will finish this part of the whole work)
A 1 work 8 hours
A 1/10 work (1/10)X8 = 4/5 hour
Hence the work will be completed in (8+ 4/5)hours = 8 4/5 hours
Answer : 8 4/5 hour
14. A can do a piece of work in 20 days ,B in 15 days and C in 12 days. How soon can the work be done if A is assisted by B on one day and by C on the next alternately?
Answer:
A 20 days 1 work,
A 1 day 1/20 work,
B 15 days 1 work,
B 1 day 1/15 work,
C 12 days 1 work,
C 1 day 1/12 work,
As A is assisted by B on first and C on the second alternately, hence:
1st day : (A+B) (1/20+ 1/15 ) work done
2nd day : (A+C) (1/20+ 1/12 ) work done
(A+B+C) 2 days (7/60+ 8/60 )=1/4 work
(A+B+C) 1 day 1/4X2 work = 1/8 work
(A+B+C) 1 work 1/(1/8) =8 days
Answer : 8 days
15. A can do a piece of work in 30 days , B in 50 days and C in 40 days. How soon can the work be done if A is assisted by B on one day and by C on the next, alternately?
Answer:
A 30 days 1 work,
A 1 day 1/30 work,
B 50 days 1 work,
B 1 day 1/50 work,
C 40 days 1 work,
C 1 day 1/40 work,
As A is assisted by B on the first day,
Work done on 1st day : (1/30 + 1/50 )= 4/75
As A is assisted by c on the second day,
Work done on 2nd day : (1/30 + 1/40 )= 7/120
Work done in 2 days = (4/75 +7/120 )= 67/600
Part of work done in 1 day =67/1200
Whole work = 1200 /67 days (approximate measure )
Hence we can conclude that the work takes at least 16 days to finish ;
No. of days’ work remaining after 16 days =(1200/67)-16 =128/67days
In 2 days, 67/600 part of the work is done
Hence in 16 days, 8X67/600 =536/600 part of the work is done
Part of the work remaining after 16 days = 1- 536/600 =64/600
Part of work done on the 17th day = 4/75
Part of work remaining after 17 days = 64/600-4/75 =8/150
Part of work done on the 18th day = 7/120
Part of work remaining after 18 days = 8/150-7/120 =-1/20
Hence it can be concluded that the work is finished on 18th day and (A+C) finish it.
(A+C) 1/120 work 1 day
(A+C) 8/150 work (120/7) x (8/150)=32/35 day
Total work is finished in = 17 + 32/35 days
=17 32/35 days
Answer: 17 32/35 days
16.A and B together can do a piece of work in 44/5 days, B and C together can do it in 8 days , and A,B,C together in 4 days. How long would A and C together take to do it ?In what time would B do it alone?
Answer:
A + B 24/5 days 1 work,
A + B 1 day 5/24 work,
B + C 8 days 1 work ,
B +C 1 day 1/8 work
C +B+ A 4 days 1 work,
C + B+ A 1 day ¼ work,
(A+B+C)-(B+C) 1 day ( ¼ - 1/8)=1/8 work
A 1 day 1/8 work
(A+B)-A 1 day (5/24 – 1/8 ) =1/12 work
B 1 day 1/12 work
B 1 work 1/ (1/12) =12 days
(B+C)-B 1 day (1/8 -1/12 =1/24) work
C 1 day 1/24 work
(A+C) 1 day (1/8 +1/24 )=1/6 work
(A+C) 1 work 6 days
Answer: B= 12 days
A+C =6 days
17.A and B together can do a piece of work in 7 days. If A does twice as much work as Bin a given time, find how long A alone would take to do the work.
Answer:
(A+B) 7 days 1 work
(A+B) 1 day 1/7 work
As A =2B,
(B+2B) 1 day 1/7 work
3B 1 day 1/7 work
B 1 day 1/7X3 work =1/21 work
Hence,
A 1 day (1/7-1/21) =2/21 work
A 1 work 1/(2/21) days= 21/2 days =10½ days
Answer : 10½ days
18. A can do a piece of work in 6 days ,B takes 8 days. C takes as long as A and B would take working together. How long will it take B and C to complete the work together?
Answer:
A 6 days 1 work,
A 1 day 1/6 work,
B 8 days 1 work,
B 1 day 1/8 work,
C 1 day (1/6+1/8) =7/24 work
(B+C) 1 day (1/8+7/24) =5/12 work
(B+C) 1 work 1/(5/12) =12/5 days = 2 2/5 days
Answer: 2 2/5 days
19. A is twice as good a workman as B ;and together they finish a work in 14 days. In how many days can it be done by each separately?
Answer:
(A+B) 14 days 1 work
(A+B) 1 day 1/14 work
As A=2B,
(B+2B) 1 day 1/14 work
3B 1 day 1/14 work
B 1 day 1/14X3 work =1/42 work
B 1 work 1/(1/42) days= 42 days
As A is twice as good as B, he would finish the work in half the time as in B;
Hence , A will finish the work in 21 days
Answer : B=42 days
A=21 days
20. C does half as much in a day as A and B can do together and B does half as much again as A. if all three working together can mow 20 hectares of barley in 16 days, how long would each, working by himself take to mow 5 hectares ?
Answer:
C =1/2( A + B) =1/2(A) + 1/2(B) = (1/2)A + ( 1/2) X (3/2) A =(1/2 +3/4 ) A =(5/4) A,
B =(1/2) A + A = (3/2)A ; C =1/2( A + B) = 1/2 (A) + 1/2(B) = 1/2(B) + (1/2 X2/3)B = 5/6(B)
A =(2/3)B
(A + B + C) 16 days 1 work,
(A + B + C) 1 day 1/16 work,
A + (3/2) A + (5/4) A 1 day 1/16 work,
(15/4) A 1 day 1/16 work,
A 1 day (1/16)/(15/4) = 1/60 work,
A 1/60 work 1 day,
A 1 work 1/(1/60) = 60 days,
A mows 20 hectares 60 days,
A mows 1 hectare 60/20 days,
A mows 5 hectare 3X5 = 15 days,
Again,
(A + B + C) 16 days 1 work,
( 2/3 ) B + B +( 5/6) B 16 days 1 work,
( 5/2) B 16 days 1 work,
B 16 days 1/(5/2) = 2/5 work,
B 1 day 2/5X16 =1/40 Work,
B 1 work (20 hectares) 1/(1/40) =40 days
B 1 hectare 40/20 days = 2 days
B 5 hectares 2X5 =10 days
Now,
A 60 days 20 hectares =1 work,
A 1 day 1/60 work,
B 40 days 20 work,
B 1day 1/20 work,
A+B 1day 1/60 + 1/40 = 1/24 work,
A+B+C 1 day 1/16 work
C 1 day 1/16-1/24 =1/48 work
C 1 work 48 days
C 20 hectares 48 days
C 1 hectare 48/20 days
C 5 hectares 48X5/20 days =12 days
Answer: A=15 days
B=10 days
C=12 days
21.If A takes half as long to do a piece of work as B takes, and C does it in the same time as A and B together ,and if all three working together would take 7 days, how long would each take separately?
Answer:
C=A+B
B=A/2
A=2B
As A and B with C can finish the work in 7 days ,
We can say that,
A+A/2 +A/2 +A= 1/7 work 1 day
3A 1/7 work 1 day
A 1/21 work 1 day
A 1 work 21 days
We can also say that,
2B+B+B+2B =1/7 work 1 day
6B 1/7 work 1 day
B 1/42 work 1 day
B 1 work 42 days
C can do the same work as (A+B) together
C 1 day 1/21+ 1/42 =1/14 work
C 1 work 14 days
Answer: A=21 days
B=42 days
C=14 days
22. A, B and C can do a piece of work in 12 days; A and C together work twice as much as B; A and B together work thrice as much as C. In what time could each do it separately?
Answer:
(A+B+C) 12 days 1 work
(A+B+C) 1 day 1/12 work
2B = (A+C)
3C= (A+B)
We can also say that,
3B=A+B+C
3B 1/12 work 1 day
B 1/36 work 1 day
B 1 work 36 days
We can say that
4C=A+B+C
Hence,
4C 1/12 work 1 day
C 1/48 work 1 day
C 1 work 48 days
B+C 1 day 1/36 +1/48 =7/144 work
A+B+C 1 day 1/12 work
A 1 day 1/12-7/144=5/144work
A 1 work 1/(144/5) days =144/5 days =28 4/5 days
Answer: A= 28 4/5 days
B= 36 days
C= 48 days
23. A,B and C can do a piece of work in 16,32 and 48 day respectively; they start working together but C leaves after working together but C leaves after working 4 days and B, 2 days before the completion of work. Find in how many days the work was finished.
Answer:
A 16 days 1 work,
A 1 day 1/16 work,
B 32 days 1 work,
B 1 day 1/32 work,
C 48 days 1 work,
C 1 day 1/48 work,
(A + B + C) 1 day (1/16 + 1/32 + 1/42) = 11/241 work,
Part of work left ( 1 – 11/24 ) = 13/24 work,
A 1 day 1/16 work,
A 2 days 2/16 =1/8 work,
Part of work left ( 13 /24 – 1/8 ) = 5/12 work,
A + B 1 day 1/16 + 1/32 = 3/32 work,
A + B 3/32 work 1 day
A + B 1 work 1/(3/32) = 32/3 day
A + B 5/12 work (32/3)X(5/12) = 40/9 = 44/9 days,
Time taken to complete the whole work =( 4 + 2 + 44/9) = 10 4/9 days.
Answer: 10 4/9 days.
24. A and B can do a piece of work in 10 days, B and C in 15 days and C and A in 20 days. They all work at it for 6 days; and then A leaves, and B and C go on together for 4 days more. If B then leaves, how long will C take to complete the work?
Answer:
A + B 10 days 1 work,
A + B 1 day 1/10 work,
B + C 15 days 1 work,
B + C 1 day 1/15 work,
C + A 20 days 1 work,
C + A 1 day 1/20 work,
(A + B + B + C + C + A) 1 day (1/10 + 1/15 + 1/20) work,
2(A + B + C) 1 day 13/60 work,
(A + B + C) 1 day (13/60)X1/2 = 13/120 work,
(A + B + C) 6 days (13/120)X6 = 13/20 work,
B + C 1 day 1/15 work,
B + C 4 days (1/15)X4 = 4/15 work,
Total work completed = (13/20 + 4/15) = 11/12
Remaining work = (1 – 11/12) = 1/12
C 1 day (13/120 – 1/10) = 1/120 work,
C 1/120 work 1 day
C 1 work 1/(1/120) = 120 day,
C 1/12 work (120X1/12) = 10 days.
Answer.10 days.
25. If A can do as much work in 4 hours as B can do in 6 hours, or as C can do in 8 hours, how long will it take C to complete a piece of work, one third of which has been done by A working 8 hours and B working 18 hours.
Answer:
A’ s 4 hour work = C’ s 8 hour work,
A’ s 1 hour work = C’ s 8/4 = 2 hour work,
A’s 8 hour work = 2 X 8 = 16 hour work,
Similarly,
B’s 6 hour work = C’s 8 hour work,
B’s 1 hour work = C’s 8/6 =4/3 hour work,
B’s 18 hour work = 18X(4/3) hour work,
1/3 of the work is completed by A working 18 hours
Time taken by C to complete 1/3 of the work = A’s 8 hour work + B’s 18 hour work
=8 X 2 + 18X4/3
=16 +24 =40 hours
Time taken by C to complete 2/3 i.e. rest of the work ={40/(1/3)}X 2/3 =40X3X2/3 = 80 hours
Answer : 80 hours
26. If A can do as much work in 3 days as C in 4 days and B in 5 days as much as C in 6 days, how long will it take B to complete a piece of work which A can finish in 18 weeks?
Answer:
A’s 3 days’ work = C’s 4 days’ work
A’s 1 days’ work = C’s 4/3 days’ work
Again,
C’S 6 days’ work =B’s 5 days’ work
C’S 1 days’ work =B’s 5/6 days’ work
C’S 4/3 days’ work =B’s 6X4/6X3 days’ work =10/9 days’ work
A’s 1 days’ work = B’s 10/9 days’ work
A’s (18X7) days’ work (as A works 18 weeks) = B’s (10/9)X18X7 days’ work
=140 days’ work =20 weeks
Answer : 20 weeks
27.A can do a piece of work in 14 days and B in 21 days. They begin together. But 3 days before the completion of work ,A leaves off. In how many days is the work completed?
Answer:
A 14 days 1 work ,
A 1day 1/14 work,
B 21 days 1 work,
B 1 day 1/21 work,
B 3 days 3/21=1/7 work (as B alone works last 3 days)
Hence remaining work =1-(1/7)=6/7 work
A+B 1 day (1/14+ 1/21) work= 5/42 work
A+B 5/42 work 1 day
A+B 1 work 42/5 days
A+B 6/7 work 42X6/5X7 days =36/5 days
Total time =3 +36/5 = 51/5 days = 10 1/5 days
Answer: 10 1/5 days
28. A,B and C can do a piece of work in12,18 and 24 days respectively: they work at it together; A stops the work after 4 days and B is called off 2 days before the work is done. In what time was the work finished ?
Answer:
A 12 days 1 work,
A 1 day 1/12 work,
B 18 days 1 work,
B 1 day 1/18 work,
C 24 days 1 work,
C 1 day 1/24 work,
(A + B + C) 1 day (1/12 + 1/18 + 1/24) = 13/72 work,
(A + B + C) 4 days (13/72)X4 =13/18 work,
In last 2 days ,C does 2/24 work =1/12 work
Hence, part of the work done by B and C in the middle = 1- (1/12 +13/18) =7/36 work
Now,
B+C (1/18+1/24)=7/72 work 1 day
B+C 1 work 72/7 days
B+C 7/36 work (72X 7)/(7X36) days= 2 days
The whole work is completed in = 4+2+2 =8 days
Answer: 8 days
29.If 3 men or 5 women can reap a field in 43 days, how long will 5 men and 6 women take to reap it?
Answer:
3 men can reap the field in =43 days
1 man can reap the field in =43X3 days
5 men can reap the field in =43X3/5 days
5 women can reap the field in =43 days
1 woman can reap the field in =43X5 days
6 women can reap the field in =43X5/6 days
Now,
5 men 43X3/5 days 1 work
5 men 1 day 5/(43X3) work
6 women 43X5/6 days 1 work
6 women 1 day 6/(43X5) work
5 men +6 women 1 day 5/(43X3) + 6/(43X5) work =1/15 work
5 men + 6 women 1 work 1/ 1/15 =15 days
Answer :15 days
30. If either 3 men or 4 women can do a certain piece of work in 43 days ,in how many days can 7 men and 5 women working together do a work twice as great ?
Answer :
3 men’s work = 4 women’s work
1 man’s work = 4/3 women’s work
7 men’s work = 4X7/3 women’s work =28/3 women’s work
4 women do the work in =43 days
1 woman does the work in =43X4 days
(28/3 +5) women do the work in =(43X4)/(28/3 +5) days = 12 days
Hence they can do a work twice as great in =12X2 =24 days
Answer: 24 days
31. If 30 men and 14 boys can reap a field in 21 days, in how many days will 20 men and 4 boys reap it, supposing that 3 men can do as much as 5 boys?
Answer:
3 men’s work = 5 boy’s work,
1 men’s work = 5/3 boy’s work,
30 men’s work = 30 X(5/3) = 50 boy’s work,
20 men’s work + 4 boy’s work = (20X5/3 + 4) boy’s work
= (112/3) boy’s work,
50 boys + 14 boys = 64 boys,
64 boys 21 days 1 work,
1 boy 21 days 21X64 work,
(112/3) boys 21 days (21X64)/(112/3) = (21 X 64 X 3)/112 =36 days.
Answer: 36 days.
32. If 5 men and 2 boys working together can do four times as much work per hour as a man and a boy together, compare the work of a man with that of a boy.
Answer:
Let the work done by 1 man be x and 1 boy be y,
According to question
5x + 2y = 4( x + y)
Or, 5x + 2y = 4x + 4y,
Or, x=2y
Hence ratio = 1:2
Answer : 1:2
33. One man, 3 women and 4 boys can do a piece of work in 96 hours;2 men and 8 boys can do it in 80 hours; and 2 men and 3 women can do it in 120 hours. In how many hours can it be done by 5 men and 12 boys?
Answer:
Let the work done by 1 man, 1 woman and 1 boy be x,y and z respectively.
Hence, according to question,
x+3y+4z=1/96
2x +8z=1/80
2x +3y=1/120
Hence, 3y= 1/80 -2x =(1-240x)/120
8z=1/80 -2x =(1-160x)/80
4z=(1-160x)/160
Therefore,
X+3y+4z =x+ (1-240x)/120 +(1-160x)/160
Or, 1/96= (7-960x)/480
Or, x= 1/480 (solving the equation)
Or, 5x = 1/96
And 2x =1/240
Also 8z = 1/80 -1/240 =1/120
& z=1/960
12z =(1/960)X12 =1/80
Hence, 5x+12z i.e. work of 5 men + work of 12 boys = 1/80 +1/96 =11/480
Hence the whole work is completed in = 1 ÷ 11/480 days =480/11 days =43 7/11 days
Answer : 43 7/11 days
34. If I must hire 2 men and 3 boys for 6 days to do the same piece of work as 11 men and 5 boys could do in 11/2 days, compare the work of a boy with that of a man.
Answer:
Let the work done by 1 man be x and 1 boy be y,
According to question,part of work done by men and boys:
2x +3y =(1/6) X11
11x +5y =(2/3) X2
Hence,
Solving the above two equations simultaneously, we get
Y=1/46 & x=7/138
Therefore,
Ratio x:y =7/138/1/46 =7/3 : y:x= 3:7
Answer : 3:7
35. 15 men would finish a piece of work in 210 days. But at the end of every 10 days 15 additional men are employed. In how many days will it be finished?
Answer:
15 men 210 days 1 work
15 men 1 day 1/210 work
15 men 10 days 10/210 =1/21 work
According to question, at the end of every 10 days 15 men are added.
Therefore, part of work done by the men every 10 days will increase by 1/21
Part of the work done in 1st 10 days =1/21
Part of the work done in next 10 days=2/21
Similarly, by trial and error calculation whole work will be done in
1/21 +2/21 +3/21 +4/21 +5/21 +6/21 =21/21 =1
(10 +10 +10 +10 +10 +10) =60 days (clear by calculating till the work is finished)
Answer : 60 days
please give answers for pg 298 ex 127
ReplyDeletea, b and c can finish a work in 10, 12 and 15 days respectively. if b stops after 2 days, how long would it take a and c to finish the remaining work?
ReplyDeletePart of the work done by A+C = 1/10+1/15 = 5/30
DeletePart of the work B have done = 12-10 = 2 or , 1/2
Therefore ,Part of the remaining work done by A and C = 5/30 - 1/2 = 1/3 = 3 days
Please solve Ex 129
ReplyDeletePl solve Ex-128
ReplyDeleteThis comment has been removed by the author.
ReplyDeletetwo trains a and b running on parallel lines enter a tunnel 2 km long at the opposite ends at the same time . they meet in 1.5 minutes and a has travelled the tunnel 400m more than b.in 4.5 seconds they cross each other and 1 min later a has completely passed through the tunnel.find the length and rate of the trains. Please give solution.
ReplyDeleteIn sum no. 22, how did you calculate 3B=A+B+C and 4C=A+B+C?
ReplyDelete