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 if 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? 

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 if 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?  Correct Answer 60 m

Below diagram shows the distance between the Prakash's house and Daksh's house:

[ alt="F1 Prashant 13.3.21 Pallavi D15" src="//storage.googleapis.com/tb-img/production/21/03/F1_Prashant_13.3.21_Pallavi_D15.png" style="width: 495px; height: 430px;">

Now, Triangle "PRQ" is a right-angled triangle, so using Pythagoras Theorem:

RP² + PQ² = RQ²

y² + (40)² = (50)²

y² = 2500 - 1600

y² = 900

y = √ 900

y = 30 m

Now, Triangle "PQS" is a right-angled triangle, so using Pythagoras Theorem:

SP2 + PQ2 = SQ2

x² + (40)2 = (50)2

x² = 2500 - 1600

x² = 900

x = √ 900

x = 30 m

The distance between the Prakash's house and Daksh's house = x + y,

= 30 m + 30 m

= 60 m

Hence, the correct answer is "60 m".