CAT Questions

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Given that 

6 men and 8 boys can do a piece of work in 10 days 

26 men and 48 boys can do the same in 2 days

As the work done is equal,

10(6M + 8B) = 2(26M + 48B)

60M + 80B = 52M + 96B

=> M = 2B

=> B = M/2 ……(1)

Now Put (1) in 15M + 20B

=> 15M + 10M = 25M

Now, 6M + 8B in 10 days

=> (6M + 4M) 10 = 100M

Then D(25M) = 100M

=> D = 4 days.

W1:A1 W2:A2 ..... WN:AN

  2 : 3                   4 : 5                    5 : 7 

W1W1+A1 = 25 W2W2+A2=49 WNWN+AN = 512

= 72/180

= 80/180

= 75/180  

 =>     5   :   3

Therefore, the ratio is  5: 3

Speed in still water = 6 kmph

Stream speed = 1.2 kmph

Down stream  = 7.2 kmph

Up Stream = 4.8 kmph

x/7.2 + x/4.8 = 1

x = 2.88

Total Distance  = 2.88 x 2 = 5.76 kms

If we count letters till the end of the alphabet including that letter in reverse order then
Here the values are nothing but the values corresponding to the alphabets when taken in a reverse order,i.e,A=26 ,B=25...,Z=1
G = 20 and O = 12 totaling 32
S = 8, H = 19 and E = 22 totaling 49

So
SOME = 8 + 12 + 14 + 22 = 56.

The Ezra Cup is a popular polo tournament conducted annually in India. The Calcutta Polo Club runs this oldest and first ever Polo Trophy. The first Ezra Cup was held in 1880. After a period of inactivity, it has now been revived by Mr. Keshav Bangur, Calcutta Polo Club's president.

Let the numbers be 3x, 3x + 3 and 3x + 6.
Then,
3x + (3x + 3) + (3x + 6) = 72
9x = 63
x = 7
Largest number = 3x + 6 = 27.

=> Second largest number = 27 - 3 = 24

Let the total distance to be covered is 84 kms.
Time taken to cover the distance without stoppage = 84/42 hrs = 2 hrs
Time taken to cover the distance with stoppage = 84/28 = 3 hrs.
Thus, he takes 60 minutes to cover the same distance with stoppage.
Therefore, in 1 hour he stops for 20 minutes.