Quantitative Aptitude: Time and Work Set 18

1. Machines A and B Produce 100 products in 10 days, Machines B and C together can produce the same products in 12 days and machines A and C
   together can produce that products in 15 days. In how many days can A produce the same products alone?
   24
   22
   21
   23
   27
   Option A
   1 day work of A and B together = 1/10 units
   1 day work of B and C together = 1/12 units
   1 day work of A and C together = 1/15 units
   1 day work of A + B and B + C and A+ C together = 1/10 + 1/12 + 1/15 units
   ie)( 2A+2B+ 2C) = 15/60 = ¼ units
   =>1 day work of (A+ B+C)= 1/8
   1 day work of A= 1 day work of ( A+B+C) – 1 day work of ( B+C)
   = 1/8 – 1/12
   = 1/24
    A can produce in 24 days
   
   
    



2. Two friends Ram and Sam can complete a project in 14 days and 35 days respectively.
   In how many days they will complete the project if they work together?
   5
   6
   10
   11
   12
   Option C
   1 day Work of Ram = 1/14
   1 day work of Sam= 1/35
   1 day work of Ram and Sam = 1/14 + 1/35 =7 /70 1/10
   =>Ram and Sam together can complete in 10 days
   
   
    



3. A can stitch a shirt in 12 hours. B and C can stitch a shirt in 9 hours while A and C together can do it in 6 hours.
   How long will B alone do the work?
   36
   33
   34
   35
   31
   Option A
   A -> 1/12 units
   B+C-> 1/9 units
   A+C-> 1/6 units
   C-> 1/6 – 1/12 = 1/12 units
   B-> 1/9 – 1/12= 1/36 units
   B can alone stitch in 36 hours
   
   
    



4. Worker 1 can complete a piece of work in 8 days. Worker 2 can complete in 10 days. Then Worker 3 also joined with them and they completed the same work in 4 days .
   Find how many days worker C alone complete the work?
   35
   36
   42
   44
   40
   Option E
   Worker 1 one day work = 1/8 units
   Worker 2 one day work = 1/10
   Workers 1+ 2+ 3 one day work = ¼
   Worker 3 one day work = 1/4 -1/8-1/10= 1/40
   =>Worker 3 can complete in 40 days alone.
   
   
    



5. Mano can construct a shop in 30 days. He works at it for 10 days and then Somu finishes in 40 days.
   In how many days taken to complete if they work together?
   10
   20
   30
   40
   50
   Option B
   Mano’s 1 day work = 1/30 units
    10 days work = 1/3 unit
    Remaining work = 1- 1/3 = 2/3 done by Somu.
    So somu’s one day work = 2/3/40 = 1/60 units
    1 day work of Mano and Somu = 1/30 + 1/60 =3/60=1/20
    So Mano and Somu can complete a work in 20 days together.
   
   
    



6. A project work could be finished in 27 days by some workers. but it was finished 9 days before the deadline
   as 10 more workers are joined. Find the number workers .
   21
   19
   18
   20
   22
   Option D
   let x be the number of workers.
   x workers can complete the work in 27 days.
   x+10 can complete the work in 18 days ( 27-9).
   ie) 27 * x = (x+ 10) * 18
   =>9x = 180
   => x=20
   
   
    



7. X can complete a piece of work in 20 days and Y can complete a work in 40 days . They began the work 10 days before finishing the work
   X leaves from the work. Find in how many days the work was completed?
   10
   12
   14
   16
   18
   Option A
   one day,
   A work ->1/20
   B work -> 1/40
   Let t be the total time to finish the work.
   =>t-10/20 + t/40 =1
   =>t/20 + t/40 = 1+1/2 = 3/2
   =>3t/20= 3/2
   =>t=10 days
   
   
    



8. A can do a work in 10 days and B in 15 days. If they work on it together for some days and 5/12 of work remains then
   find out how many days did they work together?
   3/2
   5/3
   7/2
   11/9
   7/9
   Option C
   1 day work of A= 1/10
   1 day work of B= 1/15.
   Let x be the days of work A and B together .
   x days work of A and B= x/10 + x/15
   x days work completed= 1-5/12=7/12
   x/10 + x/15 =7/12
   x/6=7/12
   =>x=7/2 days.
   
   
    



9. A takes four times as much time as B or five times as much time as C to finish a piece of work. Working together, they can finish the work in 22 days. B can do the work alone in:
   6
   5
   3
   8
   4
   Option B
   Let A takes x days to complete the work.
   B takes x/4 days to complete the work.
   C takes x/5 days to complete the work.
   A+B+C can complete the work = 1/x+4/x+5/x = 1/2
   =>10/x= 1/2
   =>x=20
   Hence B can take = 20/4 = 5 days to finish the work.
   
   
    



10. First Air cooler can cool the room in 10 minutes while second takes 15 minutes to cool under similar conditions.
    If both air coolers are switched on at same instance then how long will it take to cool the room approximately ?
    5
    7
    6
    4
    8
    Option C
    First cooler ->10 minutes
    second cooler-> 15 minutes
    Together = (a x b)/(a + b)
    = (15 x 10)/(15 + 10)
    = 150/25
    = 6 minutes