What term should be added to antecedent and subtracted from consequent of ratio `4 : 7 `to make a compound ratio of `2 : 3 " and " 5 : 4` ?

Explanation

Let the number be x.
As per question, `(4 + x) : (7 - x) = 2 xx 5 : 3 xx 4`.
`[:' " the compound ratio of the ratios " 2 : 3 " and " 5 : 4 = 2 xx 5 : 3 xx 4]`
or, ` (4 + x)/(7-x) = (2 xx 5)/(3 xx 4)`
or, ` (4 + x)/(7 -x) = 5/6 " or, " 24 + 6x = 35 - 5x`.
or, ` 6x + 5x = 35 - 24 " or, " 11x = 11`
or, ` x = 11/11 = 1`.
Hence the required number = 1.