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XAT Quants Questions




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Q #11
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Quants Question

Directions: Refer the following data to answer the questions given below.

The average age of a man, his wife and their two children is 31 years. The man is six years older than his wife and one child is two years younger to the other. If, when the younger child was born the man was 32 years old, then find the present age of his wife

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Q #12
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Quants Question

Directions: Refer the following data to answer the questions given below.

Three math classes: X, Y, and Z, take an algebra test. The average score in class X is 83. The average score in class Y is 76. The average score in class Z is 85. The average score of all sudents in classes X and Y together is 79. The average score of all students in classes Y and Z together is 81. What is the average for all the three clalsses?

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Q #13
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Quants Question

Directions: Read the following information to answer the question.

Pipe A fills a tank of 700 litres capacity at the rate of 40 litres a minute. Another pipe B fills the same tank at the rate of 30 litres a minute. A pipe at the bottom of the tank drains the tank at the rate of 20 litres a minute. If pipe A is kept open for a minute and then closed and pipe B is kept open for a minute and then closed and then pipe C is kept open for a minute and then closed and the cycle repeated, how long will it take for the empty tank to overflow?

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Solution:

Pipe A fills the tank at the rate of 40 litres a minute. Pipe B at the rate of 30 litres a minute and Pipe C drains the tank at the rate of 20 litres a minute.

If each of them is kept open for a minute in the order A-B-C, the tank will have 50 litres of water at the end of 3 minutes.

After 13 such cycles, the tank will have 13×50=650 litres of water.

It will take 13×3=39 minutes for the 13 cycles to be over.

At the end of the 39th minute, Pipe C will be closed and Pipe A will be opened. It will add 40 litres to the tank. 

Therefore, at the end of the 40th minute, the tank will have 650+40=690 litres of water.

At the end of the 40th minute, Pipe A will be closed and Pipe B will be opened. It will add 30 litres of water in a minute. 

Therefore, at the end of the 41th minute, the tank will have 690+30=720 litres of water.

But then at 700 litres, the tank will overflow. Therefore, Pipe B need not be kept open for a full minute at the end of 40 minutes.

Pipe B needs to add 10 more litres of water at the end of 40 minutes. It will take (1/3)rd of a minute to fill 10 litres of water.

Therefore, the total time taken for the tank to overflow=40 minutes +1/3 of a minute

or 40 minutes 20 seconds.


Q #14
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Quants Question

Directions: Read the following information to answer the question.

Yana and Urvashi normally work for 8 hours but do extra four hours on overtime. A job was done by 2 ladies together in 12 days in which Yana and Urvashi did overtime for few days (not necessarily same number of days). It is calculated that had Yana not done her overtime, then the work would have taken 15 days to complete and corresponding value for Urvashi is 20 days. How many days it would have taken for the work to complete had both ladies not done overtime?
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Solution:

Let the number of days required by yana to finish the work alone be x days of 8 hrs.
Let the number of days required by urvashi to finish the work alone be y days of 8 hrs.
Let the number of days of overtime by yana and urvashi be p and k respectively.
So,in 12 days yana finishes 12/x+k/2x of work.
In 12 days,urvashi finishes, 12/y+p/2y of work.
So by condition 1, 12/x+12/y+k/2x+p/2y=1....(1)
By condition 2, 15/x+15/y+p/2y=1.....(2)
And,by condition 3, 20/x+20/y+k/2x=1.....(3)
Adding 2 and 3 and subtracting 1 from the result,
1/x+1/y=1/23.

So,if both work normally,they take 23 days.


Q #15
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Quants Question

Directions: Read the following information to answer the question.

Bibhor takes 3 hours to fetch as much water as Ahmed can fetch in 2 hours. Deepak takes 5 hours to fetch as much water as Bibhor can fetch in 4 hours. A tank takes 20 hours to fill if all work together. What time would Bibhor take to fill the tank alone (in hrs)?

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Let the work done by Ahmed be 60 (LCM of 2,3,4,5)
So, work done per hour by:
Ahmed – 60/2 = 30
Bibhor – 60/3  = 20
Bibhor in 4 hours – 20 x 4 = 80
Deepak – 80/5  = 16
Therefore, total work done in an hour = 30 + 20 + 16 = 66
If all 3 work for 20 hours, total work done = 66 * 20
If Bibhor alone has to work, time taken to do 66 * 20 of work = 66 * 20/20  (work done by Bibhor in 1 hour)
= 66 hours