The cost price of 20 articles is the same as the selling price of x articles.…

Percentage profit is defined as Profit% = [(S.P. − C.P.) / C.P.] × 100. In cost-price/selling-price ratio problems like this one, it is usually easiest to assume a convenient cost price per unit and set up an equation from the given relation.

1. Let the cost price (C.P.) of 1 article be Re. 1. Then the C.P. of 20 articles = Rs. 20.

2. The C.P. of 20 articles equals the S.P. of x articles, so the S.P. of x articles = Rs. 20.

3. The C.P. of x articles (at Re. 1 each) = Rs. x, so the profit on selling x articles = S.P. − C.P. = 20 − x.

4. Using Profit% = (Profit / C.P.) × 100: 25 = [(20 − x) / x] × 100.

5. 25x = 100(20 − x) → 25x = 2000 − 100x → 125x = 2000 → x = 16.

Cross-check with the ratio method: a 25% profit means S.P. : C.P. = 5 : 4 per article. Since the C.P. of 20 articles equals the S.P. of x articles, 20 × C.P.(1) = x × S.P.(1) = x × (5/4) × C.P.(1), which gives x = 20 × 4/5 = 16 — the same value, confirming the result.

Hence x = 16.