Question 11 - Figure it out - Page 28, 29, 30 - Chapter 1 Class 8 - Fractions in Disguise (Ganita Prakash II)

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Question 11 If the length of a rectangle is increased by 10% and the area is unchanged, by what percentage (exactly) does the breadth decrease by?Let Original Length = L Original Breadth = B Thus, Original Area = Original Length × Original Breadth = L × B Now, Given that the length of a rectangle is increased by 10% and the area is unchanged Thus, New Length = Original Length + 10% × Original Length = L + 𝟏𝟎/𝟏𝟎𝟎 × L = L + 1/10 × L = L + 0.1 × L = L × (1 + 0.1) = L × 1.1 And, New Area = Old Area = L × B We need to find New Breadth Now, New Area = New Length × New Breadth Putting values L × B = (L × 1.1) × New Breadth L × B = L × 11/10 × New Breadth (𝐿 × 𝐵 × 10)/(𝐿 × 11) = New Breadth New Breadth = (𝑳 × 𝑩 × 𝟏𝟎)/(𝑳 × 𝟏𝟏) New Breadth = (𝐵 × 10)/11 New Breadth = B × 𝟏𝟎/𝟏𝟏 We need to find how much Breadth decreased by Since no values are given, we have to find it in Percentage Now, Percentage breadth decreased = (𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑏𝑟𝑒𝑎𝑑𝑡ℎ)/(𝑂𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝐵𝑟𝑒𝑎𝑑𝑡ℎ) × 100 = (𝑶𝒓𝒊𝒈𝒊𝒏𝒂𝒍 𝒃𝒓𝒆𝒂𝒅𝒕𝒉 − 𝑵𝒆𝒘 𝑩𝒓𝒆𝒂𝒅𝒕𝒉)/(𝑶𝒓𝒊𝒈𝒊𝒏𝒂𝒍 𝑩𝒓𝒆𝒂𝒅𝒕𝒉) × 100 = (𝐵 − 𝐵 ×10/11)/𝐵 × 100 = 𝐵( 1 − 10/11)/𝐵 × 100 = (𝟏−𝟏𝟎/𝟏𝟏) × 100 = ((11 − 10)/11) × 100 = (1/11) × 100 = 100/11 = 9.09..% Thus, breadth decreased by approximately 9.09%