Quantitative Aptitude - Arithmetic Ability Questions

Let the number of buffaoes be x and number of ducks be y.

Then 4x + 2y = 2(x + y) + 24  

=> 2x = 24

=> x = 12.

The ratio of their investments:
50000x36 : 80000x30 = 3 : 4
Simran's share of profit = (24500x3/7) = Rs.10,500.

By investing Rs 128, income derived = Rs. 16

By investing Rs. 100, income derived =Rs. (16/128*100)  = Rs.12.5

Interest obtained  = 12.5%

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.

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.

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

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

= (2 x 434)sq.cm  = 868 sq.cm