Boats & Streams set 2
Q1. A boat goes downstream at a speed of 10 km/h and returns upstream at a speed of 5 km/h. What is its average speed ? Q17. āĻāĻāĻ¨ āĻ¨āĻžā§ąā§ āĻ¸ā§āĻāĻ¤ā§° āĻĻāĻŋāĻļāĻ¤ 10 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻž āĻŦā§āĻā§ āĻ¯āĻžāĻ¯āĻŧ āĻā§°ā§ āĻāĻāĻ¤āĻŋ āĻ āĻšāĻžā§° āĻ¸āĻŽāĻ¯āĻŧāĻ¤ āĻ¸ā§āĻāĻ¤ā§° āĻŦāĻŋāĻĒā§°ā§āĻ¤ā§ 5 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻž āĻŦā§āĻā§ āĻāĻšā§āĨ¤ āĻāĻ¯āĻŧāĻžā§° āĻāĻĄāĻŧ āĻŦā§āĻ āĻāĻŋāĻŽāĻžāĻ¨ ?
Options / āĻŦāĻŋāĻāĻ˛ā§āĻĒ: (a) 7 km/h (b) 7.5 km/h (c) 6.67 km/h (d) None of these / āĻāĻ¯āĻŧāĻžā§° āĻā§āĻ¨ā§āĻā§ āĻ¨āĻšāĻ¯āĻŧ
Ans / āĻāĻ¤ā§āĻ¤ā§°: (c) 6.67 km/h
Formulla (āĻ¸ā§āĻ¤ā§ā§°) for Average Speed / āĻāĻĄāĻŧ āĻŦā§āĻā§° {(When equal distances are covered at speeds x and y: (āĻ¯ā§āĻ¤āĻŋāĻ¯āĻŧāĻž āĻ¸āĻŽāĻžāĻ¨ āĻĻā§ā§°āĻ¤ā§āĻŦ x āĻā§°ā§ y āĻŦā§āĻā§ āĻ āĻ¤āĻŋāĻā§ā§°āĻŽ āĻā§°āĻž āĻšāĻ¯āĻŧ:)}
Average Speed = 2xy / x+y
Soln / āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨
Here, x = 10 km/h , y = 5 km/h
Average Speed = (2 × 10 × 5) / 10 + 5 = 100/15 = 6.67 km/h
Average Speed = 6.67 km/h (āĻāĻĄāĻŧ āĻŦā§āĻ = 6.67 āĻāĻŋāĻŽāĻŋ/āĻāĻŖā§āĻāĻž)