Question

Anil travelled 300 km by bus and 200 km by taxi. For this, it took him 5 hours and 30 minutes. However if he travels 260 km by bus and 240 km by taxi then he takes 6 minutes more. The speed of the bus is ________km/hour

• A. 100
• B. 120
• C. 80
• D. 110

Answer 1

The Correct Option is A

To find the speed of the bus, we need to set up two equations based on the information provided: 

1. Let the speed of the bus be \(x\) km/hr and the speed of the taxi be \(y\) km/hr.
2. According to the first scenario:
   • Anil travels 300 km by bus and 200 km by taxi in 5 hours and 30 minutes.
   • Convert the time to hours: 5 hours and 30 minutes = 5.5 hours.
   • The time taken by the bus is \(\frac{300}{x}\) hours.
   • The time taken by the taxi is \(\frac{200}{y}\) hours.
   • Hence, the equation is: \(\frac{300}{x} + \frac{200}{y} = 5.5\)
3. According to the second scenario:
   • Anil travels 260 km by bus and 240 km by taxi, taking 6 minutes more than the first scenario.
   • 6 minutes more = 5.5 hours + 0.1 hours = 5.6 hours.
   • The time taken by the bus is \(\frac{260}{x}\) hours.
   • The time taken by the taxi is \(\frac{240}{y}\) hours.
   • Hence, the equation is: \(\frac{260}{x} + \frac{240}{y} = 5.6\)
4. We now have two equations:
   • (1) \(\frac{300}{x} + \frac{200}{y} = 5.5\)
   • (2) \(\frac{260}{x} + \frac{240}{y} = 5.6\)
5. To solve these equations:
   • Subtract equation (1) from equation (2):
     • \((\frac{260}{x} + \frac{240}{y}) - (\frac{300}{x} + \frac{200}{y}) = 5.6 - 5.5\)
     • \(\frac{260}{x} - \frac{300}{x} + \frac{240}{y} - \frac{200}{y} = 0.1\)
     • \(-\frac{40}{x} + \frac{40}{y} = 0.1\)
     • \(\frac{40}{y} = \frac{40}{x} + 0.1\)
     • \(\frac{40}{y} - \frac{40}{x} = 0.1\)
   • Rearranging gives:
     • \(0.1xy = 40(x - y)\)
   • Solving for \(x\) using trial for options.
     • Plug \(x = 100\) into the equation and solve for \(y\) using either (1) or (2):
       • For equation (1): \(\frac{300}{100} + \frac{200}{y} = 5.5\)
       • \(3 + \frac{200}{y} = 5.5 \Rightarrow \frac{200}{y} = 2.5 \Rightarrow y = 80\)
     • Both \(x = 100\) and \(y = 80\) satisfy the second equation (2), hence the speed of the bus is 100 km/hr.

Thus, the speed of the bus is 100 km/hr.