A pipe of diameter ‘d’ can drain a certain water tank in 40 minutes. The time taken by a pipe of diameter ‘2d’ for doing the same job is :

Solution
Cross sectional area of first pipe =\(\pi r_{1}^{2}=\pi \left ( \frac{d}{2} \right )^{2}\)
Cross sectional area of second pipe =\(\pi r_{2}^{2}=\pi d^{2}\)
Now,
\(\Rightarrow \frac{x}{40}=\frac{\pi d^{2}/4}{\pi d^{2}}\)
\(\Rightarrow x=40\times \frac{1}{4}= 10 \: min.\)
From the given choices, select the one which can be formed by using the letters of the given word :MEASUREMEN

Solution
Measurement
option (1)MASTER can be formed by above
From the given choices, select the one which can be formed by using the letters of the given word :TRANSFORMATIO

Solution
Given word TRANSFORMATION
Option;
Option(3) INFORMANT may be formed using the letters of given word
X told Y, “It is true that I am your real brother, but you are not my sister”. How would Y be possibly related to X ?

Solution
X is real brother of Y
but Yis not x's Sister
⇒ Y must be x's Brother
A is the father of X Bis the mother of Y. The sister of X and Z is Y. Which of the following state ments is not true?

Solution
option (1)is true.
option (2)is true.
option (3)is false as y is daughter of A
option (4)May be true or false.
x may be sister or brother of z.
Pointing to a woman a man said “Her mother is the only daughter of my mother.” How is the man related to the woman?

Solution
Man is maternal uncle of the woman.
Preeti has a son, named Arun.Ram is Preeti’s brother. Neeta too has a daughter named Reema.Neeta is Ram’s sister. What is Arun’s relationship to Reema?

Solution
Thus Arun is cousin of Reema.
Visitors to a show were charged Rs. 150.00 each on the first day, Rs. 75.00 on the second day and Rs. 25.00 on the third day and the total attendance on the three days were in the ratio 2 : 5 : 13. The average charge per person for the whole show is :

Solution
Let the number ofpersons on
three days be 2x, 5x and 13x respectively.
∴ Required average\(=\frac{2x \times 150+ 5x\times 75 + 13x\times 25}{2x+5x+13x}\)
\(=\frac{300x + 375x + 325x}{20x}\)
\(=\frac{1000x}{20x}= Rs. 50\)
Onefourth of a certain journey was covered at an average speed of 45 km/hour, one third at the speed of 48 km/hour and the remaining journey at the speed of 50 km/hour. The average speed of the whole journey in m/hour is :

Solution
Average speed
\(=\frac{Total distance}{Time taken}\)
\(=\frac{1}{\frac{\left ( \frac{1}{4} \right )}{45}+\frac{\frac{1}{3}}{48}+\frac{\left ( 1\frac{1}{4}\frac{1}{3} \right )}{50}}\)
\(=\frac{1}{\frac{1}{180}+\frac{1}{144}+\frac{1}{120}}\)
\(=\frac{1}{\frac{4 + 5 + 6}{720}}=\frac{720}{15}= 48 kmph\)
The average age of 8 persons in a committee is increased by 2 years when two men whose ages are 35 years and 45 years are replaced by two women. The average age of two women is (in years)

Solution
\(\frac{w_{1}+w_{2}}{2}=\frac{35+45+2\times 8}{2}\)
= 48 years