Quantitative Aptitude - Arithmetic Ability Questions

In a simultaneous throw of two dice, n(S) = 6 x 6 = 36

Let E = event of getting a doublet = { (1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}

 P(E)=n(E)n(S)=636=16

If a number to be divisile by 88, it should be divisible by both "8" and "11"

Check for '8' :
For a number to be divisible by "8", the last 3-digit should be divisible by "8"
Here 72x23y --> last 3-digit is '23y'
So y=2 [ (i.e) 232 is absolutely divisible by "8"]

Chech for '11' :
For a number to be divisible by "11" , sum of odd digits - sum of even digits should be divisible by "11"
(7 + x + 3) - (2 + 2 + y)
(7 + x + 3) - (2 + 2 + 2)
(10 + x) - 6 should be divisible by "11"
for x = 7
=> 17 - 6 = 11 [ which is absolutely divisible by "11"]

So x = 7 , y= 2.

By hit and trail, we find that

47619 x 7 = 333333.

7) 333333 (47619
    333333
----------------
        0

And 476190476 x 7 = 3333333333 but smallest number is 47619.

We know that, R = (100 x S.I) / (P x T)

Now I gives, S.I = Rs. 4000.

        II gives,  T = 4 years.

But, P is unknown. So, we cannot find R.

So, given data is insufficient to get R.

7x5: 5xk = 7:10
k = 10 months

Let the pipe B be closed after 'K' minutes.

30/16 - K/24 = 1 => K/24 = 30/16 - 1 = 14/16

=> K = 14/16 x 24 = 21 min.

504/M = 384/800

(504 x 800) / 384 = M

M = 1050