Question

what should be subtracted from each of the numbers 54,71,75,99 so that the reminders may be proportional?

Answer 1

Assume that x be number subtracted from each of the numbers 54,71,75 and 99 so that the remainders may be proportion.  

∴ 54 - x , 71 - x , 75 - x , and 99 - x are in proportion.

(54 - x) / (71 - x) = (75 - x) / ( 99 - x)

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

x2 - 99x - 54x + 5346 = x2 - 75x - 71x + 5325
(x² cancel from both side)

  - 153x + 5346 = -146x + 5325

153x- 146x = 5346 - 5325

7x = 21

∴ x = 3.

∴ When x = 3 subtracted from each of the numbers so that the remainders may be proportion.
are u understand?