Question 10 - Figure it out - Page 67, 68 - Chapter 3 Class 8 - Proportional Reasoning-2 (Ganita Prakash II)

Transcript

Question 10 A small pump can fill a tank in 3 hours, while a large pump can fill the same tank in 2 hours. If both pumps are used together, how long will the tank take to fill?Given that Small pump takes 3 hours to fill the tank Thus, we can write Tank filled by small pump in 1 hour = 𝟏/𝟑 And, Large pump takes 2 hours to fill the tank Thus, we can write Tank filled by large pump in 1 hour = 𝟏/𝟐 Now, they do the work together Let Time taken to complete work together = x hours Thus, Tank filled by Small pump in x hours + Tank filled by Large pump in x hours = Total volume of tank In these questions, we take Total volume of tank = 1 So, our equation becomes Tank filled by Small pump in x hours + Tank filled by Large pump in x hours = 1 Tank filled by Small pump in 1 hour × 𝑥 + Tank filled by Small pump in 1 hour × 𝑥 = 1 1/3 × 𝑥 + 1/2 × 𝑥 = 1 𝒙/𝟑+𝒙/𝟐 = 1 (2 × 𝑥 + 3 × 𝑥)/(3 × 2) = 1 (2𝑥 + 3𝑥)/6 = 1 5𝑥/6 = 1 𝒙=𝟔/𝟓 𝒙= 1.2 hours Thus, it will take them 𝟔/𝟓 hours to finish the whole thing. And, 𝟔/𝟓 hours = 1+𝟔/𝟓 × 60 minutes = 𝟔/𝟓 × 60 minutes= 1 hour + 𝟏/𝟓 × 60 minutes = 1 hour + 12 minutes = 1 hour and 12 minutes. Or we can write It will take them 1 hour and 12 minutes to finish the whole thing.