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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


Team Careers360 19th Jan, 2024
Answer (1)
Team Careers360 22nd Jan, 2024

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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