Arithmatical - Time and Work

DIRECTIONS : Problems based on time and work.
1. A, B and C together earn Rs.300 per day, while A and C together earn Rs.188 and B and C together earn Rs.152. The daily earning of C is
  A.  Rs.10
  B.  Rs.40
  C.  Rs.68
  D.  Rs.112
Solution
B’s daily earning= Rs.(300 – 188)
= Rs. 112.
A’s daily earning= Rs.(300 – 152)
= Rs. 148.
C’s daily earning= Rs.[300 -(112 + 148)]
= Rs. 40.
2. Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by tanya to do the same piece of work is
  A.  15
  B.  16
  C.  18
  D.  25
Solution
Ratio of times taken by Sakshi and Tanya=125:100
= 5 : 4.
Suppose Tanya takes x days to do the work.
= 5 : 4 :: 20 : x
x = (4×20/5)
  = 16 days.
Hence, Tanya takes 16 days to complete the work.
3. Kim can do a work in 3 days while David can do the same work in 2 days. Both of them finish the work together and get Rs.150. What is the share of Kim?
  A.   Rs.30
  B.   Rs.60
  C.   Rs.70
  D.   Rs.75
Solution
Kim's wages : David's wages= Kim's 1 day's work : David's 1 day's work
= 1/3 : 1/2
= 2 : 3
Kim's share= Rs.(2/5×150)
= Rs.60.
4. 5 men and 2 boys working together can do four times as much work as a man and a boy. Working capacities of a woman and a boy are in the ratio
  A.  1 : 2
  B.  1 : 3
  C.  2 : 1
  D.  3 : 1
Solution
Let 1 man's 1 day’s work= x
and 1 boy's 1 day’s work= y
Then, 12x+16y=1/5
13x+24y=1/4
Solving these two equations, we getx= 1/100 and y=1/200
Required ratio= x : y
= 1/100 : 1/200
= 2 : 1
5. A man can do a job in 15 days. His father takes 20 days and his son finishes it in 25 days. How long will they take to complete the job if they all work together?
  A.  Less than 6 days
  B.  exactly 6 days
  C.  appro. 6.4 days
  D.  more than 10 days
Solution
1 day's work of the three persons= (1/15+1/20+1/25)
47/300.
So, all the three together will complete the work in = 300/47
= 6.4 days.
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