Question

There are two routes to travel from the place A to B by bus. The first bus reaches the place B via C and the second bus reaches the place B from A directly. The position of A, B and C are represented in the following graph.

Based on the above information, answer the following questions.

If the fare for first bus is Rs 10 per km, then what is the fare for total journey by that bus?

• A. Rs 85
• B. Rs 38
• C. Rs 45
• D. Rs 54

Answer 1

The correct option is A Rs 85

The total distance travelled by the first bus is AB + BC.

By Distance formula, $AC=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$
On substituiting the values,
$AC=\sqrt{(3+2{)}^2+(2+3{)}^2}\Rightarrow AC=\sqrt{5^2+5^2}\Rightarrow AC=\sqrt{25+25}\Rightarrow AC=5\sqrt{2}km$

Similarly,
$BC=\sqrt{(3-2{)}^2+(2-3{)}^2}\Rightarrow BC=\sqrt{1+1}\Rightarrow BC=\sqrt{2}km$

Total distance $=AC+BC=5\sqrt{2}+\sqrt{2}=6\sqrt{2}km$
Total distance = 8.48 km
Total fare $=8.48\times 10=Rs.84.8$
Total fare = Rs. 85 (Approximately)