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Original breadth of a rectangular box is 20 cm. The box was then remade in such a way that its length increased by 30% but the breadth decreased by 20% and the area increased by 100 cm2. What is the new area of the box?

Original breadth of a rectangular box is 20 cm. The box was then remade in such a way that its length increased by 30% but the breadth decreased by 20% and the area increased by 100 cm2. What is the new area of the box? Correct Answer 2600 cm<sup>2</sup>

Given∶

Original breadth of the rectangular box = b = 20 cm

Percentage increase in length = 30%

Percentage decrease in breadth = 20%

Calculation∶

Let original length of the rectangular box be l.

⇒ Original area of rectangular box = lb = 20l

⇒ Length of the rectangular box after 30% increase = 130/100 × l

⇒ Breadth of the rectangular box after 20% decrease = 80% of b = 80/100 × 20 = 16 cm

⇒ New Area of the rectangular box = 130/100 × l × 16

According to the question,

New Area of the rectangular box = Original area of rectangular box + 100

⇒ 130/100 × l × 16 = 20l + 100

⇒ l(20.8 – 20) = 100

⇒ 0.8l = 100

⇒ l = 1000/8 = 125 cm

∴ New Area of the rectangular box = 130/100 × l × 16 = 130/100 × 125 × 16 = 130 × 20 = 2600 cm2

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