Question : Directions: Nirav's house is 40 m south of Akash's house. Daksh's house is to the east of Akash's house in a straight line at a distance of X m. Prakash's house is to the west of Akash's house in a straight line at a distance of Y m. If the shortest distance between Prakash's house and Nirav's house is 50 m and the shortest distance between Daksh's house and Nirav's house is also 50 m, then what is the distance between Prakash's house and Daksh's house?
Option 1: 40 m
Option 2: 30 m
Option 3: 60 m
Option 4: 80 m
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Correct Answer: 60 m
Solution : Firstly, we will draw the diagram as per the given instructions –
Now, we have the distance between between Prakash's house and Daksh's house.
From the above diagram,
Using the Pythagoras theorem, we can find the values of X and Y –
(40)
2
+ (Y)
2
= (50)
2
1600 + (Y)
2
= 2500
(Y)
2
= 2500 – 1600
(Y)
2
= 900
Y = 30
Similarly,
(40)
2
+ (X)
2
= (50)
2
1600 + (X)
2
= 2500
(X)
2
= 2500 – 1600
(Y)
2
= 900
X = 30
So, the value (X + Y) = 30 + 30 = 60m. Hence, the third option is correct.
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