Question 3 - Figure it out - Page 175 - Chapter 7 Class 8 - Proportional Reasoning-1(Ganita Prakash)

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Question 3 Blue and yellow paints are mixed in the ratio of 3 : 5 to produce green paint. To produce 40 mL of green paint, how much of these two colours are needed? To make the paint a lighter shade of green, I added 20 mL of yellow to the mixture. What is the new ratio of blue and yellow in the paint?First let us answer the first part of the question To produce 40 mL of green paint, how much of these two colours are needed? Given ratio of Blue and yellow paints is 3 : 5 So, we can write Amount of Blue paint : Amount of Yellow Paint = 3 : 5 Converting into fractions (𝑨𝒎𝒐𝒖𝒏𝒕 𝒐𝒇 𝑩𝒍𝒖𝒆 𝑷𝒂𝒊𝒏𝒕)/(𝑨𝒎𝒐𝒖𝒏𝒕 𝒐𝒇 𝒀𝒆𝒍𝒍𝒐𝒘 𝑷𝒂𝒊𝒏𝒕)=𝟑/𝟓 Cross multiplying Amount of Blue Paint = 𝟑/𝟓 × Amount of Yellow Paint Now, Total paint = 40 mL Amount of Blue Paint + amount of Yellow Paint = 40 Putting Amount of Blue Paint = 3/5 × Amount of Yellow Paint 𝟑/𝟓 × Amount of Yellow Paint + Amount of Yellow Paint = 40 Amount of Yellow Paint × (3/5+1) = 40 Amount of Yellow Paint × ((3 + 5)/5) = 40 Amount of Yellow Paint × (8/5) = 40 Amount of Yellow Paint = 40 × 5/8 Amount of Yellow Paint = 5 × 5 Amount of Yellow Paint = 25 mL Thus, Amount of Blue Paint = 3/5 × Amount of Yellow Paint = 3/5 × 25 = 3 × 5 = 15 mL Now, our question is To make the paint a lighter shade of green, I added 20 mL of yellow to the mixture. What is the new ratio of blue and yellow in the paint? Since Blue paint doesn’t change Amount of Blue paint = 15 mL And, after adding 20 mL yellow paint to already 25 mL we get New Amount of Yellow paint = 25 + 20 = 45 mL Thus, new ratio of blue and yellow paint is 15 : 45 Simplifying ratio 15 : 45 = 15/45 = 1/3 = 1 : 3 Thus, the new ratio is 1 : 3