The price of two articles are in the ratio of 3 : 2 respectively. The price of first article is increased by 40% and the price of second article is decreased by x%. If the new ratio of the price of the two articles is 7 : 3 respectively, then what is the value of x?

Let the price of two articles be Rs.300 and Rs.200
Price of first article is increased by 40%.
New price of first article = 120% of 300 = $$\dfrac{120}{100}\times300 = Rs.420$$
Price of second article is decreased by x%
New price of second article = (100-x)% of Rs.200 = $$\dfrac{100-x}{100}\times200 = Rs(200-2x)$$
Given, $$\dfrac{420}{200-2x} = \dfrac{7}{3}$$

=> $$\dfrac{60}{200-2x} = \dfrac{1}{3}$$

=> $$180 = 200-2x$$
=> $$2x = 20$$
=> $$x = 10$$