What must be subtracted from each of the numbers 26, 44, 56 and 104 so that the remainders are in proportion?

Concept Used: ​

Simple ratio and proportion

Let the remainders be (26 - x), (44 - x), (56 - x), (104 - x)

Since the remainders must be in proportion,

​$$\frac{26 - x}{44 - x} = \frac{56 - x}{104 - x}$$​​

(26 - x)(104 - x) = (44 - x)(56 - x)

​$$(26 \times 104) - 26x - 104x + x^2 = (44 \times 56) - 44x - 56x + x^2$$​​

​$$2704 - 130x + x^2 = 2464 - 100x + x^2$$​​

2704 − 130x = 2464 −100x

2704 – 2464 = 130x−100x

240=30x

​$$x = \frac{240}{30} = 8$$​​

Thus, the number that must be subtracted from each of the given numbers is 8.