Example 6 (Page 66) - Chapter 3 Class 8 - Proportional Reasoning-2 (Ganita Prakash II)

Transcript

Example 6 (Page 66) If Ram takes 1 hour to cut a given quantity of vegetables and Shyam takes 1.5 hours to cut the same quantity of vegetables, how much time will they take to cut the vegetables if they do it together?Given that Ram takes 1 hour to cut a given quantity of vegetables Thus, we can write Work completed by Ram in 1 hour = 1 And, Shyam takes 1.5 hours to cut the same quantity of vegetables Thus, we can write Work completed by Shyam in 1.5 hours = 1 Work completed by Shyam in 1 hours = 1/1.5 = 1/(15/10) = 10/15 = 𝟐/𝟑 Now, they do the work together Let Time taken to complete work together = x hours Thus, Work done by Ram in x hours + Work done by Shyam in x hours = Total work done In these questions, we take Total work done = 1 So, our equation becomes Work done by Ram in x hours + Work done by Shyam in x hours = 1 Work done by Ram in 1 hour × 𝑥 + Work done by Shyam in 1 hour × 𝑥 = 1 1 × 𝑥 + 𝟐/𝟑 × 𝑥 = 1 𝒙+𝟐𝒙/𝟑 = 1 (3 × 𝑥 + 2𝑥)/3 = 1 (3𝑥 + 2𝑥)/3 = 1 5𝑥/3 = 1 𝒙=𝟑/𝟓 Thus, f they cut the vegetables together, they will finish in 3/5 hours.