Example 12 - Chapter 7 Class 8 - Proportional Reasoning-1(Ganita Prakash)

Transcript

Example 12 A mixture of 40 kg contains sand and cement in the ratio of 3 : 1. How much cement should be added to the mixture to make the ratio of sand to cement 5 : 2?Let’s find out how many kilograms of Sand and Cement are there in 40kg mixture with 3 : 1 ratio Given ratio of sand and cement is 3 : 1 So, we can write Amount of Sand : Amount of Cement = 3 : 1 Converting into fractions (𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑆𝑎𝑛𝑑)/(𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝐶𝑒𝑚𝑒𝑛𝑡)=3/1 Amount of Sand = 3 × Amount of Cement Now, Total Weight = 40kg Amount of Sand + Amount of Cement = 40kg Putting Amount of Sand = 3 × Amount of Cement 3 × Amount of Cement + Amount of Cement = 40 Amount of Cement × (3 + 1) = 40 Amount of Cement × 4 = 40 Amount of Cement = 40/4 Amount of Cement = 10kg And, Amount of Sand = 3 × Amount of Cement = 3 × 10 = 30kg The Change: We want a new ratio of 5 : 2, but we are only adding cement. The amount of Sand (30 kg) stays the same! The Calculation: In the new ratio (5 : 2), the "5" part represents the Sand. We know the Sand is 30 kg So, 5 parts = 30 kg 1 part = 30 ÷ 5 = 6 kg Therefore, the Cement (which is 2 parts) must be 2 × 6 = 12 kg Final Step: We need 12 kg of cement total. We already have 10kg. Since 12 – 10 = 2 kg Thus, We need to add 2 kg of cement.