Quantitative Aptitude - Arithmetic Ability Questions

Let pipe A takes p min to fill

Then,

pipe B takes 3p min to fill

=> 3p - p = 32

=> p = 16 min => 3p = 48 min

Required, both pipes to fill = (48 x 16)/(48 + 16) min = 12 min.

we can do this by trial and error method.

Putting x = 2,we get 2²(2² - 1) = 12.
checking with other integers, the above equation always gives a value which is a multiple of 12,
So, x²(x² - 1) is always divisible by 12.

Given there are 9 flavours of ice creams.

Each child takes the combination of two flavours and no two children will have the same combination

This can be done by  ways i.e children.

Number of children=C29  = 9 x 8 / 1x 2 = 36.

The year 1996 is a leap year. So, it has 2 odd days. So, the day on 17th March, 1997 will be 2 days beyond the day on 17th March,1996.

Here 17th March, 1997 is Monday. So, 17th March, 1996 is Saturday.

Let the ratio be x : (x + 40), then ,

xx+40=27 

 7x = 2x + 80 

 x = 16 

Required ratio = 16 : 56

Suppose age of each women be W and average age of 12 men be x

Hence , each woman's age = 24 years