What should be subtracted from each of the no. 54, 71, 75 and 99 so that the remainder may be in proportion.

3

Best approach is to check the options:

Like, option (b) = 3

If we subtract 3 from each number, it becomes in proportion.

(54 -  3) : (71 - 3) :: (75 - 3) : (99 - 3)

51 : 68 :: 72 : 96

3 :  4 :: 3 : 4 (justify)

Therefore, 3 is correct answer.

Alternate approach:

\(\frac{54-x}{71-x}=\frac{75-x}{99-x}\)        

(54 – x) (99 – x) = (75 – x) (71 – x)              

x² – 99x – 54x + 5346 = x² – 75x – 71x + 5325

– 153x + 146x = –5346 + 5325

          –7x = – 21

⸫  x = 3