The prices of two articles are in the ratio 4 : 5. If the price of the first article is increased by x% and that of the other is decreased by 30%, then the new prices of A and B will be in the ratio 10 : 7. The value of x is:

Ratio of price of two articles = 4 : 5

Let the price of two articles are 4p and 5p respectively

The price of the first article is increased by x%

New price of the first article = $$\frac{100+x}{100}\times$$4p

The price of the second article is decreased by 30%

New price of the second article = $$\frac{70}{100}\times$$5p

Ratio of the new prices of articles = 10 : 7

$$\Rightarrow$$  $$\frac{\frac{100+x}{100}\times4p}{\frac{70}{100}\times5p}=\frac{10}{7}$$

$$\Rightarrow$$  $$\frac{\left(100+x\right)\times4}{70\times5}=\frac{10}{7}$$

$$\Rightarrow$$  $$\frac{\left(100+x\right)\times2}{10\times5}=\frac{5}{1}$$

$$\Rightarrow$$  200 + 2x = 250

$$\Rightarrow$$  2x = 50

$$\Rightarrow$$  x = 25

Hence, the correct answer is Option C