A towel was 75 cm broad and 120cm long. When bleached, it was to have lost 40% of its length and 20% breadth. The percentage of decrease in area is:

Solution

Original area = 75 × 120 = 9,000 sq cm. Reduced length = 60% of 75 cm = 45 cm Reduced breadth = 80% of 120 cm = 96 cm Reduced area = 45 × 96 = 4,320 sq cm Reduction in area = 9,000 – 4,320 = 4,680 sq m. ∴ % Reduction = 4,680/(9,000 ) × 100 = 52%. SHORTCUT ALTERNATE METHOD: LET LENGTH OF RECTANGLE = 100 AND BREADTH OF RECTANGLE = 100 SO AREA = L×B = 100×100 = 10000 SO NEW LENGTH OF RECTANGLE = 60 AND BREADTH OF RECTANGLE = 80 SO AREA = L×B = 60×80 = 4800 ∴ % Reduction = (10000-4800)/10000× 100 = 5200/10000× 100 = 52%.