Five girls are standing in a ground at a certain distance. Rekha and Beena are 18 m apart from each other. Veena is standing somewhere in the mid of Rekha and Beena. Pinky is standing 5 m North to Rekha. Rekha is 12 m West to Veena. Yamini is standing 8 m South to Beena. What is the shortest distance between Pinky and Yamini ?
- (1)33 m
- (2)31 m
- (3)23 m
- (4)13 m
Answer
Why
RPSC deleted this question in its final answer key, so no option is marked correct.
The stem places five girls by distance and direction and asks for the shortest distance between Pinky and Yamini. The method: fix one girl at the origin, mark each girl's position, then use Pythagoras for the straight line.
Place Rekha at (0, 0), with east as +x and north as +y.
Step 1 — Veena.
"Rekha is 12 m West to Veena", so Veena = (12, 0).
Step 2 — Beena.
Rekha and Beena are 18 m apart, and Veena stands somewhere between them. Read with the three girls on one east–west line, Beena = (18, 0), 6 m east of Veena.
Step 3 — Pinky and Yamini.
Pinky, 5 m north of Rekha = (0, 5)
Yamini, 8 m south of Beena = (18, −8)
Step 4 — the gaps between Pinky and Yamini.
East–west: 18 − 0 = 18 m
North–south: 5 + 8 = 13 m
Step 5 — Pythagoras.
Distance² = 18² + 13² = 324 + 169 = 493
Distance = √493 ≈ 22.2 m
The idea to remember: the shortest distance is the straight line; square the east–west and north–south gaps, add them, and take the square root.
Why the others are wrong
- (1)33 m — Option (1) offers 33 m. RPSC's final key marks no option.
Set against the one-line reading: a path from Pinky to Yamini along the two gaps measures 18 + 13 = 31 m. A straight line between two points is never longer than a path joining them, and 33 m is longer than that 31 m path.
- (2)31 m — Option (2) offers 31 m. RPSC's final key marks no option.
31 m equals 18 m + 13 m, the east–west gap plus the north–south gap between Pinky and Yamini on the one-line reading. That is the length of a path along the two directions; the straight line uses √(18² + 13²).
- (3)23 m — Option (3) offers 23 m. RPSC's final key marks no option.
On the one-line reading the straight-line distance is √493 ≈ 22.2 m. A distance of exactly 23 m would need the squared gaps to add up to 23² = 529.
- (4)13 m — Option (4) offers 13 m. RPSC's final key marks no option.
13 m equals 5 m + 8 m, the north–south gap alone: Pinky is 5 m north of the Rekha–Veena–Beena line and Yamini 8 m south of it. A straight-line distance is at least as long as each of its gaps, and the east–west gap on the one-line reading is 18 m.
Concept
Direction-sense reasoning turns words into positions. Fixing one person at the origin, with east and north as the positive directions, makes each distance-and-direction clue a step along one axis.
"X is 12 m west of Y" puts X 12 m to the left of Y on the east–west axis; "5 m north" moves up the north–south axis.
The shortest distance between two points is the straight line joining them. With an east–west gap a and a north–south gap b, it is √(a² + b²), by Pythagoras' theorem.
RPSC's 2023 syllabus lists "Direction sense test" under Mental Ability in Reasoning & Mental Ability.
Map grids use the same coordinate method: a place is given by how far east and how far north it lies from a reference point, its easting and northing.
Pythagoras' theorem, a² + b² = c² for a right-angled triangle with hypotenuse c, then turns the two grid gaps into a straight-line distance.
Key facts
- Shortest distance = √(east–west gap² + north–south gap²), by Pythagoras' theorem.
- With Rekha at (0, 0): Veena (12, 0) and Pinky (0, 5); on the one-line reading, Beena (18, 0) and Yamini (18, −8).
- On that reading the gaps are 18 m and 13 m, and the distance is √493 ≈ 22.2 m.
- A path along both gaps (18 + 13 = 31 m) is longer than the straight line joining the same two points.
- Pythagorean triples include 3-4-5, 5-12-13, 8-15-17 and 7-24-25.
RPSC deleted this question; the card marks no option.
Study next
Common traps
- Adding the gaps instead of using Pythagoras. 18 + 13 = 31 m is a path along two directions, not the shortest distance.
- Counting only one gap. 5 + 8 = 13 m is the north–south gap; the 18 m east–west gap still has to enter the calculation.
- Measuring from the wrong girl. Pinky is placed from Rekha and Yamini from Beena; Veena's 12 m only fixes where Veena stands.
A question can place several people by distance and direction and ask for the shortest distance between two of them, as this one does.
A question can also trace one walker's turns and ask for the final direction or the distance from the starting point.
Related PYQs
Mr. X starts walking towards south from point A. After walking 20 m., he reaches at point B. Now he turns left and walks 20 m and reaches at point C. Now he turns 45° anticlockwise, walks a distance 20√3 m and reaches at the point D. What is the shortest distance between point A and point D ?
- (1) 20√3 m
- (2) 40 m
- (3) 20√5 m
- (4) 40√3 m
Answer(3)
Same shortest-distance reasoning with Pythagoras. There one walker goes 20 m south, turns left for 20 m, then turns 45° anticlockwise for 20√3 m, and the shortest distance from the start is asked (RPSC's key: option (3), 20√5 m); this deleted 2023 question places five girls and asks for the distance between two of them.
Practice
- practice — not a real PYQ
Point B is 12 m east of point A. Point C is 5 m north of A. Point D is 4 m south of B. What is the shortest distance between C and D ?
- (a)21 m
- (b)15 m
- (c)17 m
- (d)9 m
Answer(2) — With A at (0, 0): C = (0, 5) and D = (12, −4). The gaps are 12 m east–west and 5 + 4 = 9 m north–south, so the distance is √(144 + 81) = √225 = 15 m.Option (1) adds the gaps (12 + 9), option (3) adds 12 and 5, and option (4) is the north–south gap alone.
- practice — not a real PYQ
Ravi walks 6 km north, then 8 km east, then 6 km south. How far is he from his starting point ?
- (a)20 km
- (b)10 km
- (c)8 km
- (d)14 km
Answer(3) — The 6 km north and the 6 km south cancel, leaving only the 8 km east. Option (1) adds all three walks, option (2) is his distance from the start after the first two walks, √(36 + 64), and option (4) adds 6 and 8.