Read the given information carefully and answer the question below. Five…
2025
Read the given information carefully and answer the question below.
Five friends — Teenu, Bani, Chandni, Dev and Joy — are playing Hide and Seek and are standing at random points.
Bani is to the northeast of Joy.
Dev is 20 m to the east of Joy.
Joy is 60 m to the west of Teenu.
Chandni is to the northwest of Dev, in line with Joy and Bani.
Dev is 40 m to the south of Bani.
If Bani wants to look for Teenu, what distance does she save by going straight to Teenu instead of first going to Dev and then reaching Teenu?
- A.
42.47 m
- B.
56.60 m
- C.
27.34 m
- D.
23.44 m
Attempted by 19 students.
Show answer & explanation
Correct answer: D
Concept:
When people or places are related only through compass directions (north, south, east, west) and stated distances, plot every point on an x-y grid with East and North as the positive axes, and use the Pythagorean theorem, distance = √(Δx2 + Δy2), to find the straight-line distance between any two points. When a question asks how much distance is 'saved' by a direct route compared with an indirect one, that saving equals (sum of the legs of the indirect route) minus (the direct straight-line distance).
Application (this item):
Take Joy as the origin (0, 0) of the grid.
Dev is 20 m east of Joy, so Dev sits on Joy's east-west line, 20 m to its east.
Joy is 60 m west of Teenu, so Teenu also sits on that same east-west line, 60 m east of Joy — this puts Teenu 60 minus 20 = 40 m east of Dev.
Dev is 40 m south of Bani, so Bani sits directly above Dev on the same north-south line, 40 m to its north.
These facts place a right angle at Dev: one leg, Bani-Dev, runs 40 m north-south; the other leg, Dev-Teenu, runs 40 m east-west.
The route via Dev therefore covers Bani to Dev to Teenu = 40 m + 40 m = 80 m.
The direct route, Bani to Teenu, is the hypotenuse of that right triangle: √(402 + 402) = √3200 = 40 × √2. Using the standard exam approximation √2 (roughly 1.414), this works out to about 56.56 m.
Distance saved = via-route minus direct route = 80 minus 56.56 = 23.44 m, matching the option given.
Cross-check:
Because both legs of the triangle are equal (40 m each), it is an isosceles right triangle, so the hypotenuse must be exactly 40 × √2 -- this independently confirms the direct distance without re-deriving it from scratch. (Carrying √2 to more decimal places, 1.41421 rather than 1.414, gives a direct distance of about 56.57 m and a saving of about 23.43 m -- within a rounding hair of the 23.44 m option, the tiny gap coming purely from how many decimal places of √2 are carried through the working.) The setup is also consistent with the passage's own clue that Bani is to the northeast of Joy: with Bani placed 20 m east and 40 m north of Joy, Bani is indeed both east and north of Joy, i.e., in the northeast direction, confirming the coordinate placement is correct.
So the distance Bani saves by taking the direct route to Teenu instead of going via Dev is 23.44 m.