CAT Questions

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1 man's 1 day work = 1/108
12 men's 6 day's work = 1/9 x 6 = 2/3

Remaining work = 1 - 2/3 = 1/3

16 men's 1 day work = 1/108 x 16 = 4/27
4/27 work is done by them in 1 day.

1/3 work is done by them in 27/4 x 1/3 = 9/4 days.

LCM of (80, 85, 90) can be found by prime factorizing them.

80 → 2 × 2 × 2 × 2 × 5

85 → 17 × 5

90 → 2 × 3 × 3 × 5

L.C.M of (80,85,90) = 2 × 2 x 2 × 2 × 3 × 3 × 5 × 17

= 16 x 9 x 85

= 144 x 85

= 12240

L.C.M of (80,85,90) = 12240.

M is 8th from the top.

H is (50 - 20 + 1 =) 31 st from the top.

  Number of students between M and H = (31 - 8- 1=)22

Let the side of the square be x. Then, its diagonal = 2x.  

Radius of incircle = x/2  and radius of circumcircle =2x2 .

Therefore, required ratio = πx24:πx22 = 14:12=1:2

We know that   Speed=distancetime 

distance= speed * time

⇒ d=40×518×9

   d= 100 mts.

Quantity of fruit juice in the mixture = 70 - [70 x (10/100) ]= 63 litres.

After adding water, juice would form 87.5% of the mixture.

Hence, if quantity of mixture after adding x liters of water, [(87.5) /100 ]*x = 63 => x = 72 

Hence 72 - 70 = 2 litres of water must be added.

The pattern is 32+42=52,  52+122=132, 72+242=252 

The next number = 82+152=172

 i.e. 17