Question

To go from A to B, Ram goes 5 mi south, 6 mi east, 7 mi south and 2 mi west to reach B; Shyam chooses the shortest path to reach B from A. What is the total distance travelled by the two?
A. 32.65
B. 33.42
C. 34.00
D. 34.42

Answer 1

Hint: To solve this question, use the directions such as north in the upward direction, south in downward, east in right and west in left and make the path directions as directed in the question to get the answer.

Complete step-by-step answer:

In the question, we have been given that Ram goes 5 miles south, 6 miles east, 7 miles south and 2 miles west to reach B, whereas Shyam chooses the shortest path to reach B from A. We have to find the total distance travelled by the two of them.

We will first draw the figure, by taking the directions as follows, north in upward direction, south in downward direction, east in right direction and west in left direction. Now, we will follow the step by step directions given in the question to draw the figure as given below.

The path taken by Ram to reach B from A is depicted with the darker or thickened line in the figure and the lighter line is the path taken by Shyam to complete the shortest path. Now, looking at the above figure, we can clearly make out that place B is 12 miles south and 4 miles right of place A. So, by using Pythagoras Theorem, we can find the distance or the shortest distance travelled by Shyam. So, the length of the path is $\sqrt{{{\left( 12 \right)}^{2}}+{{\left( 4 \right)}^{2}}}=\sqrt{144+16}=\sqrt{160}=12.65miles$. Hence, we get the distance travelled by Shyam as 12.65 miles. Now we can calculate the distance travelled by Ram. According to the question, Ram travelled 5 miles + 7 miles + 2 miles, which is equal to 20 miles. So, the distance travelled by Ram is 20 miles and Shyam is 12.65 miles.
Therefore, the total distance travelled by both of them is 20 miles + 12.65 miles = 32.65 miles.

Hence, the correct answer is option A.

Note: The students should use the directions properly while making the direction path, because any mistake in that will result in a wrong diagram and thus the wrong answer too.