A chair is sold at a profit of 30%. If the cost price and selling price were…

Concept: When both the cost price (CP) and selling price (SP) of an item are reduced by the same amount, the absolute profit (SP − CP) stays exactly the same — only the profit PERCENTAGE changes, because percentage profit is measured relative to CP, and CP (the base) has shrunk. If CP = x and profit is p%, then SP = x(1 + p/100). Here "profit would be 18% more" is read as 18 percentage points more (30% -> 48%), which is the standard reading in this problem type — confirmed below because it is the only reading that lands on one of the given options.

1. Let the original cost price be Rs. x. Since the profit is 30%, the original selling price = 1.3x.

2. Both CP and SP are reduced by Rs. 720: new CP = x − 720, and new SP = 1.3x − 720.

3. The new profit is 18 percentage points higher than before, i.e. 30% + 18% = 48%. So: (new SP − new CP) / new CP = 48/100.

4. Substitute: [(1.3x − 720) − (x − 720)] / (x − 720) = 48/100, which simplifies to 0.3x / (x − 720) = 0.48.

5. Cross-multiply: 0.3x = 0.48x − 345.6, so 0.18x = 345.6, giving x = 1920.

Cross-check: with CP = Rs. 1920, original SP = 1.3 × 1920 = Rs. 2496 (30% profit, confirmed). New CP = 1920 − 720 = Rs. 1200, new SP = 2496 − 720 = Rs. 1776. New profit % = (1776 − 1200)/1200 × 100 = 576/1200 × 100 = 48%, which is indeed 18 percentage points more than 30%. Both conditions hold, confirming the cost price is Rs. 1920. Note also that the absolute profit amount is unchanged at Rs. 576 both before and after (2496 − 1920 = 576 and 1776 − 1200 = 576) — only the percentage rose, because it is now measured against the smaller base of Rs. 1200 instead of Rs. 1920.