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

Let the numbers are $$x$$ and $$y$$

According to questions,  Ratio of $$x$$ and $$y$$ are $$7:5$$

$$\therefore \frac{x}{y}=\frac{7}{5}$$

$$\Rightarrow y=\frac{5x}{7}$$

After diminishing both of them by 40, Ratio becomes $$27:17$$

$$\therefore \frac{(x-40)}{(y-40)} = \frac{27}{17}$$

$$\Rightarrow 17(x-40)=27(y-40)$$

$$\Rightarrow 17x - 17\times40 = 27y - 27\times40$$

$$\Rightarrow 27y - 17x=27\times40 - 17\times40$$

$$\Rightarrow 27y - 17x=40\times(27-17)$$

$$\Rightarrow 27y - 17x=400$$

Putting value of $$y$$ in above equation,

$$\Rightarrow 27(\frac{5x}{7}) - 17x=400$$

$$\Rightarrow \frac{135x}{7} - 17x=400$$

$$\Rightarrow \frac{135x-119x}{7}=400$$

$$\Rightarrow 16x=2800$$

$$\Rightarrow x=\frac{2800}{16}=175$$

$$\Rightarrow y=\frac{5x}{7}=\frac{5\times175}{7}=5\times25=125$$

$$\therefore$$ Difference b/w both numbers =$$ 175-125=50$$