Directions: Read the following information to answer the question.
Solution:
12 men in 36 days can do a work.
1 man in a day can do 1/12×36 work.
8 men in 20 days can do 8×20/12×36=10/27 work.
Similarly, we find that 20 women in 20 days can do 10/27 work.
Remaining work =7/27
Now, because in 60 days a work is done by 20 women.
In 1 day a work done by 20×60 women.
In 4 days 7/27
work is done by 20×60×7/27×4
= 70 women.
Directions: Read the following information to answer the question.
Solution:
Let 'a' be the number of days in which A can do the job alone. Therefore, working alone, A will complete (1/a)th of the job in a day.
Similarly, let 'b' be the number of days in which B can do the job alone. Hence, B will complete (1/b)th of the job in a day.
Working together, A and B will complete (1/a+1/b)th of the job in a day.
The problem states that working together, A and B will complete the job in 7.5 or 15/2 days. i.e they will complete 2/15)th of the job in a day.
Therefore, 1/a+1/b=2/15 ...... (1)
From the question, we know that if A completes half the job working alone and B takes over and completes the next half, they will take 20 days.
As A can complete the job working alone in 'a' days, he will complete half the job, working alone, in
a/2 days.
Similarly, B will complete the remaining half of the job in b/2 days.
Therefore, a/2+b/2=20
⇒ a+b=40 or a=40–b ...... (2)
From (1) and (2) we get,
{1/40−b}+1/b=2/15
⇒ 600=2b(40−b)
⇒ 600=80b−2b2
⇒ b2−40b+300=0
⇒ (b−30)(b−10)=0
⇒ b=30 or b=10.
If b=30, then a=40−30=10 or
If b=10, then a=40−10=30.
As A is more efficient than B, he will take lesser time to do the job alone. Hence A will take only 10 days and B will take 30 days.
Note: Whenever you encounter work time problems, always find out how much of the work can 'A' complete in a unit time (an hour, a day, a month etc). Find out how much of the work can be completed by 'B' in a unit time. Then add the amount of work done by A and B to find the total amount of work that will be completed in a unit time.
If 'A' takes 10 days to do a job, he will do (1/10)th of the job in a day.
Similarly, if (2/5)th of the job is done in a day, the entire job will be done in 5/2days.
Directions: Read the following information to answer the question.
Solution:
C’s one day’s work =(1/3)−(1/6+1/8)=1/24
Therefore, A:B:C = Ratio of their one day’s work =1/6:18:1/24
=4:3:1
A’s share =Rs.600×(4/8)=300
B’s share =Rs.600×(3/8)=225
C’s share =Rs[600−(300+225)]= Rs 75
Directions: Read the following information to answer the question.
Solution:
From the given information Q is thrice as efficient as P.
R is thrice as efficient as Q.
S is thrice efficient as R.
If work done by P in a day is 'n' units, the work done in a day by Q, R and S would be 3n, 9n and 27n units respectively.
It can be seem that, P,Q and R working together can do 13n units in a day while P,Q and S working together can do 31n units in a day.
Hence, the ratio of times taken to complete the work by the former and later groups is 31:13
P,Q and S take 13 days.
Directions: Read the following information to answer the question.
Solution:
Let the total distance to be covered be d
On each day under normal weather conditions they travel d/20
of the distance.
On 1st day they would travel =d/20
On 2nd day they would travel =0.8×d/20
On 3rd day they would travel =0.8×(0.8×d/20)
Let he will reach the point B in nth day
⇒ d/20+0.8 *d/20+0.82*d/20+…….+0.8n*d/20=d
⇒ d/20×(−(0.8)n+1)/(−0.8+1)=d
⇒ 1−(0.8)n=4(0.8)n=−3
Since (0.8)n>0, thus it is never equal to -3
The man will never reach the point B.