Quantitative Aptitude - Arithmetic Ability Questions

From the given data,

12 children 16 days work,
One child’s one day work = 1/192.

8 adults 12 days work,
One adult’s one day’s work = 1/96.

Work done in 3 days = ((1/96) x 16 x 3) = 1/2

Remaining work = 1 – 1/2 = 1/2

(6 adults+ 4 children)’s 1 day’s work = 6/96 + 4/192 = 1/12

1/12 work is done by them in 1 day.

1/2 work is done by them in 12 x (1/2) = 6 days.

Let the edge of the cube be a.  

 so, the diagonal  a3 = 63    

=> a=6 

 Surface area = 6a2 = 6 x 6 x 6 = 216 sq.cm

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.

 Surface area = [2 (16 x 14 + 14 x 7 + 16 x 7)] sq.cm

= (2 x 434)sq.cm  = 868 sq.cm

Let,

no. of rice bowl = x
no. of dal bowl = y
no. of meat bowl = z

Then, x + y + z = 65 ....(1)

Also given that, 2x = 3y = 4z

substituting value of y & z in terms of x i.e. y = 2x/3 and z = x/2 in eq (1),
We get x = 30.

As 1 rice bowl is shared between 2 guests,
Therefore, there are 60 guests.

          2000xX100 + 4000xY100 = 320

and     2000xX100 + 10000xY100 = 680

x = 4  and  y = 6

x-y = -2

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

Hence , each woman's age = 24 years