The tea is poured three times from the cup before it is emptied.

    If 100 is the capacity of the saucer, ( it is always to be filled only to 90 level).

-    the first time, tea poured is 90 

-    the second time tea poured is 75

-    the third time tea poured is 75

-    Total tea is 240

This is 90% of the capacity of the cup. So, capacity of the cup = 240/0.9 = 266^2/3

Ratio of the capacities of cup & sauces 

= 266^2/3: 100

= 2^2/3   : 1 = ^8/3 :   1 = 8  : 3

Answer : Rs 72

20% of A : 30% of B : 25% of C = 4 : 9 : 10. Solve to get the answer.

Let, hundred’s digit = x,

Ten’s digit = y and units digit = z

x + y = z + 1 -------------------(1)

x2 + 1 = y -----------------------(2)

x2  + y2  = z2  - 7 ----------------(3)

x + x2  + 1= z + 1

⇒ z = x2 + x

⇒ z2 = x4 + 2x3 + x2---------------(4)

Also, x2 + (x2 +1)2 = x4 + 2x3 + x2 –7 

⇒ 2 x3 - 2 x2 = 8 x3 - x2  - 4 = 0

⇒  (x-2) (x2 + x + 2) = 0

x = 2, (since x2 + x + 2 = 0 gives imaginary roots)

∴ From (2),  y = (2)2 x2

⇒ Z =  x + y – 1 = 2 + 5 – 1 = 6

∴The number is 256   

Note : The best approach here is clearly back substitution from the given answer choices.