Two numbers are in the ratio 5 : 7. On diminishing each of them by 40, they become in the ratio 17 : 27. The difference of the number is

Let the two numbers be X and Y. According to question:

$(\Rightarrow \frac{X}{Y} = \frac{5}{7})$

⇒ 7X = 5Y ….(1)

On diminishing each of them by 40 we get the new numbers as (X - 40) and (Y - 40). Hence, according to the question the new ratio is:

$(\Rightarrow \frac{{X - 40}}{{Y - 40}} = \frac{{17}}{{27}})$

⇒ 27X – 17Y – 400 = 0 …(2)

Solving the above two equations we get,

⇒ X = 125 and Y = 175

Hence, the difference of the numbers = 175 – 125

= 50