Abus travelled from village A to village B at a speed of 40 km per hou

1.	Abus travelled from village A to village B at a speed of 40 km per hour. On thereturn journey its speed was 60 km per hour. What is the average speed of thebus during the entire journey?(1) 50 km/h (2) 48 km/h (3) 46 km/h (4) 45 km/h
Answer» Given : • A bus travelled from village A to village B at a speed of 40 km per hour. • On the return journey its speed was 60 km per hour. To calculate : • Average speed during the entire journey. Calculation : Let the distance from A to B be d km. We know that, $\bigstar \: \boxed{\sf {Average \: Speed = \dfrac{<klux>TOTAL</klux> \: Distance}{Total \: time \: taken} }} \\$ $\underline{ \underline{ \sf \red {Calculating \: total \: distance \: \: :}} }$ Firstly it travels from A to village B and then it returns from B to A. ➠ Distance from A to B = d ➠ Distance from B to A = d ➛ Total Distance = Distance from A to B + Distance from B to A ➛ Total Distance = ( d + d ) km ➛ Total Distance = 2d km $\underline{ \underline{ \sf \red{Calculating \: total \: time \: \: :}} }$ As we know that, $\bigstar \: \boxed{\sf { Time = \dfrac{Distance}{Speed} }} \\$ Time taken to COVER the distance from A to B (t₁): ➠ t₁ = $\sf { \dfrac{d}{40} }$ hrs Time taken to cover the distance from B to A (t₂): ➠ t₂ = $\sf { \dfrac{d}{60} }$ hrs ➛ Total time = t₁ + t₂ ➛ Total time = $\sf { \dfrac{d}{40} + \dfrac{d}{60} }$ hrs ➛ Total time = $\sf { \dfrac{3d + 2d}{120} }$ hrs ➛ Total time = $\sf { \dfrac{5d}{120} }$ hrs ➛ Total time = $\sf { \dfrac{1d}{24} }$ hrs $\sf { \dfrac{d}{24} }$ ➛ Total time = hrs Now, SUBSTITUTING the VALUES in the formula of average speed to find the average speed of the bus during the entire journey. $\bigstar \: \boxed{\sf {Average \: Speed = \dfrac{Total \: Distance}{Total \: time \: taken} }} \\$ ➛ Average speed = $\sf{ \dfrac{2d}{ \cfrac{d}{24} }}$ km/h ➛ Average speed = $\sf{ 2 \not{d} \times \dfrac{24}{\not{d}}}$ km/h ➛ Average speed = $\sf{ 2 \times 24 }$ km/h ➛ Average speed = 48 km/h Therefore, average speed of the bus during the entire journey is 48 km/h. Option ⑵ is correct.