An order was placed for supply of carpet of breadth 3 metre, the length of carpet was 1.44 times of breadth. Subsequently the breadth and length were increased by 25 and 40 percent respectively. At the rate of 45 per square metre, what would be the increase in the cost of the carpet? (Bank P.O., 2009)

### Concept & Area and Cost Calculation Calculate the original area and the new area after percentage increases, find the difference (increase in area), and multiply by the rate to find the total increase in cost. Formula: $$Area = l \times b$$ $$Cost = Area \times Rate$$ ### Step-by-Step Solution * **Original Dimensions:** Breadth $b = 3$ m. Length $l = 1.44 \times 3 = 4.32$ m. * Original Area $= 3 \times 4.32 = 12.96$ sq. m. * **New Dimensions:** Breadth is increased by 25%. New breadth $= 3 \times (1 + 0.25) = 3 \times 1.25 = 3.75$ m. * Length is increased by 40%. New length $= 4.32 \times (1 + 0.40) = 4.32 \times 1.4 = 6.048$ m. * New Area $= 3.75 \times 6.048 = 22.68$ sq. m. * **Increase in Area:** $22.68 - 12.96 = 9.72$ sq. m. * **Increase in Cost:** Increase in Area $\times$ Rate $= 9.72 \times 45$. * $9.72 \times 45 = 437.40$. * The increase in cost is ₹ 437.40. ### Exam Strategy & Shortcut Use fractions for easier multiplication: $l = 1.44 \times 3 = 4.32$. Original Area $= 3 \times 4.32 = 12.96$. Increase in $b$ by 25% means multiplier is $5/4$. Increase in $l$ by 40% means multiplier is $14/10 = 7/5$. New Area $= (3 \times 5/4) \times (4.32 \times 7/5) = 3 \times 4.32 \times (35/20) = 12.96 \times 1.75 = 22.68$. Difference $= 22.68 - 12.96 = 9.72$. Cost $= 9.72 \times 45 = 437.4$. ### Common Pitfall Calculating the cost of the new carpet entirely and forgetting to subtract the original cost to find the *increase* is a frequent oversight. ### Final Answer Therefore, the correct answer is **₹ 437.40**.