Question : Directions: Manohar cycles X km towards the west and then turns right and cycles Y km to reach his office. Now, the shortest distance between the starting point and his office is 13 km. What can be the value of X and Y, respectively, (in km)?
Option 1: 12 and 5
Option 2: 8 and 5
Option 3: 11 and 6
Option 4: 6 and 7
Correct Answer: 12 and 5
Solution : Firstly, we will draw the diagram as per the given instructions –
As we have the shortest distance provided in the question, so applying the Pythagoras theorem in the given options, we can find the values of X and Y. Let's check the options – First option: 12 and 5 ⇒(12) 2 + (5) 2 = (13) 2 144 + 25 = 169 169 = 169 Second option: 8 and 5 ⇒(8) 2 + (5) 2 = (13) 2 64 + 25 = 169 89 ≠ 169 Third option: 11 and 6 ⇒(11) 2 + (6) 2 = (13) 2 121 + 36 = 169 157 ≠ 169 Fourth option: 6 and 7 ⇒(6) 2 + (7) 2 = (13) 2 36 + 49 = 169 85 ≠ 169 So, only the first option satisfies the given equation, X = 12 and Y = 5. Hence, the first option is correct.
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