Question

what number should be subtracted from each of the numbers 54, 71, and 99 so that the remainders may be proportional

Answer 1

let that number be X
54-x : 71-x :: 71-x: 99-x

(54-x)(99-x) =(71-x)^2

now solve this..you will get answers

Answer 2

let that number is x
now
54-x : 71-x:: 71-x:99-x
so
(54-x)(99-x) = (71-x)(71-x)
or
5346-54x+x^2-99x= 5041-71x-71x+x^2
or
5346 - 153x= 5041 - 142x
or
5346-5041 = -142x+153x
or
305= 11x
or
x= 305÷11
x=27.8 approx