A bus passes two persons moving in the direction of the moving bus at a speed of 3 km/hr and 5 km/hr

Q: What is the correct answer for CUET UG Quantitative Aptitude?

The correct answer is C. Let the speed of the bus be V km/hr. Let the length of the bus be L meters. Convert speeds to m/s: Bus speed = $V \text{ km/hr} = V \times \frac{5}{18} \text{ m/s}$. Person 1 speed = $3 \text{ km/hr} = 3 \times \frac{5}{18} = \frac{5}{6} \text{ m/s}$. Person 2 speed = $5 \text{ km/hr} = 5 \times \frac{5}{18} = \frac{25}{18} \text{ m/s}$. When the bus passes a person moving in the same direction,

Q: A bus passes two persons moving in the direction of the moving bus at a speed of 3 km/hr and 5 km/hr, respectively. The bus passes the first person in 10 s and the second person in 11 s. Find the…

The correct answer is C. Let the speed of the bus be V km/hr. Let the length of the bus be L meters. Convert speeds to m/s: Bus speed = $V \text{ km/hr} = V \times \frac{5}{18} \text{ m/s}$. Person 1 speed = $3 \text{ km/hr} = 3 \times \frac{5}{18} = \frac{5}{6} \text{ m/s}$. Person 2 speed = $5 \text{ km/hr} = 5 \times \frac{5}{18} = \frac{25}{18} \text{ m/s}$. When the bus passes a person moving in the same direction,

Q: What are the options for this CUET UG Quantitative Aptitude question?

A. 28 km/hr · B. 27 km/hr · C. 25 km/hr · D. 24 km/hr

Question

A bus passes two persons moving in the direction of the moving bus at a speed of 3 km/hr and 5 km/hr, respectively. The bus passes the first person in 10 s and the second person in 11 s. Find the speed of the bus.

FirstInTest · Accepted Answer

Let the speed of the bus be V km/hr.
Let the length of the bus be L meters.

Convert speeds to m/s:
Bus speed = $V 	ext{ km/hr} = V 	imes \frac{5}{18} 	ext{ m/s}$.
Person 1 speed = $3 	ext{ km/hr} = 3 	imes \frac{5}{18} = \frac{5}{6} 	ext{ m/s}$.
Person 2 speed = $5 	ext{ km/hr} = 5 	imes \frac{5}{18} = \frac{25}{18} 	ext{ m/s}$.

When the bus passes a person moving in the same direction, the relative speed is (Bus speed - Person speed).
Distance covered = Length of the bus (L).
Time = Distance / Relative Speed.

Case 1: Bus passes Person 1 (speed 3 km/hr) in 10 s.
Relative speed = $(V - 3) 	ext{ km/hr} = (V - 3) 	imes \frac{5}{18} 	ext{ m/s}$.
$L = (V - 3) 	imes \frac{5}{18} 	imes 10 \quad \dots(1)$

Case 2: Bus passes Person 2 (speed 5 km/hr) in 11 s.
Relative speed = $(V - 5) 	ext{ km/hr} = (V - 5) 	imes \frac{5}{18} 	ext{ m/s}$.
$L = (V - 5) 	imes \frac{5}{18} 	imes 11 \quad \dots(2)$

Equate (1) and (2) since L is the same:
$(V - 3) 	imes \frac{5}{18} 	imes 10 = (V - 5) 	imes \frac{5}{18} 	imes 11$
Cancel $\frac{5}{18}$ from both sides:
$10(V - 3) = 11(V - 5)$
$10V - 30 = 11V - 55$
$55 - 30 = 11V - 10V$
$25 = V$

So, the speed of the bus is 25 km/hr.

Answer

28 km/hr

Answer

27 km/hr

Answer

25 km/hr

Answer

24 km/hr

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