Directions: Refer the following data to answer the questions given below.
Directions: Refer the following data to answer the questions given below.
Let the average age of people aged 51 years and above be x years.
Let the average age of people aged below 51 years be y years.
Let the number of people aged below 51 years be N.
Given, the average age of all the people in the apartment complex is 38 years.
Therefore,
x?30?y?N? 38 ….(1)
30?N
We want to maximize y, which occurs when x is minimum i.e. for x=51.
Substituting the value of x in (1) we get
390=N×(38-y)
Again, when y is maximum, N is also maximum i.e. 39
Therefore maximum value of y = 28.
Directions: Read the following information to answer the question.
There are four varieties of pipes Pipe A, Pipe B, Pipe C and Pipe D. Each pipe can be either an inlet pipe or an outlet pipe but cannot be both. there are 5 tanks of equal volume.
Tank P is filled by Pipe A and Pipe B
Tank Q is filled by Pipe A and Pipe C
Tank R is filled by Pipe A and Pipe D
Tank S is filled by Pipe B and Pipe C
Tank T is filled by Pipe C and Pipe D
Time taken for the first 3 tanks (P, Q and R) to get filled are in the ratio 1:2:4 and the time taken for the S and T tanks to be filled are in the ratio 7:10.
Find the outlet pipes among the 4 varieties.
Solution:
Let A,B,C and D do a,b,c and d with of work in an hour.
Let A and B fill the tank in 1 hour.
Then A and C would fill the tank in 2 hours while A and D in 4 hours.
a+b=1 ---------- (i)
a+c=1/2 ----------- (ii)
a+d=1/4 ------------ (iii)
Let B and C take 7k hours while c and D take 10k hours to fill the tank
⇒ b+c=1/7k --------------- (iv)
c+d=1/10k -------------- (v)
a=[(i)+(ii)−(iv)]/2 = [(ii)+(iii)−(v)]/2
⇒ a={1+1/2−1/7k}/2={1/2+1/4−1/10k}/2 ---------- (vi)
⇒ k=4/70
On substituting value of k in equation (vi) we get a<0
⇒ a<0,b>0,c>0 and d>0
Hence only A is the outlet pipe.
Directions: Read the following information to answer the question.
A fill pipe can fill a tank in 20 hours, a drain pipe can drain a tank in 30 hours. If a system of n pipes (fill pipes and drain pipes put together) can fill the tank in exactly 5 hours, which of the following are possible values of n (More than one option could be correct)?
3 fill pipes cancel out 2 drain pipes. Plus, you need an additional 4 fill pipes fill the tank in 5 hours. so the answer has to be 5k + 4.
Both 54 and 29 are possible.
Directions: Read the following information to answer the question.
A is kept open for all t minutes and fills one-third the tank. Or, A should be able to fill the entire tank in '3t' minutes.
A and B together can fill the tank completely in t minutes. A alone can fill it in 3t minutes.
A and B together can fill 1/t of the tank in a minute. A alone can fill 1/3t of the tank in a minute. So, in a minute, B can fill 1/t – 1/3t = 2/3t
Or, B takes 3t/2 minutes to fill an entire tank.
To fill one-third the tank, B will take t/2 minutes. B is kept open for t - 10 minutes.
t/2 = t - 10, t = 20 minutes.
A takes 60 minutes to fill the entire tank, B takes 30 minutes to fill the entire tank. A is kept open for all 20 minutes. B is kept open for 10 minutes.
C, which is kept open for 8 minutes also fills one-third the tank. Or, C alone can fill the tank in 24 minutes.