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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