A square park P Q R S of side 90 ~m is so located that its diagonal P R is from north to south and the corner Q is to the west of S. Radha and Mohan start walking along the sides from Q and R respectively in clockwise and anti-clockwise directions with speeds of 8 ~km / hr and 10 ~km / hr. Where will they cross each other the second time ? Option 1: On PS at a distance of 30 ~m from P Option 2: On Q R at a distance of 10 ~m from Q Option 3: On PS at a distance of 30 ~m from S Option 4: On QR at a distance of 10 ~m from R

Answer: On QR at a distance of 10 ~m from R. Solution: Note: Each side is 90m Radha and Mohan start from Q and R, at 8km/h and 10km/h respectively. When they first meet, they will have collectively travelled 270m (excluding the 90m of QR) Let's take the ratios of their speed =8:10=4:5 So, Radha covers =4/(4+5)x270=4/9x270=120m and Mohan covers the remaining 150m. Hence, they meet at PS, when Radha is 60m far from S, and Mohan is 30m from P. Now, for their second meeting, they will both collectively cover 360m. Taking ratios again, Radha will cover =4/9x360=160m and Mohan will cover the remaining 200m So, they meet at QR, where Radha and Mohan are 10m from R (or 80m from Q).

Logical Reasoning

Puzzles

Hard

A square park $P Q R S$ of side $90 \mathrm{~m}$ is so located that its diagonal $P R$ is from north to south and the corner $Q$ is to the west of $S$ . Radha and Mohan start walking along the sides from $Q$ and $R$ respectively in clockwise and anti-clockwise directions with speeds of $8 \mathrm{~km} / \mathrm{hr}$ and $10 \mathrm{~km} / \mathrm{hr}$ . Where will they cross each other the second time ?

On $PS$ at a distance of $30 \mathrm{~m}$ from $P$

On $Q R$ at a distance of $10 \mathrm{~m}$ from $Q$

On $PS$ at a distance of $30 \mathrm{~m}$ from $\mathrm{S}$

On $QR$ at a distance of $10 \mathrm{~m}$ from $\mathrm{R}$

✅ Correct Option: 4

Solution figure for JIPMAT 2024 LR question 21 (Logical Reasoning)

Note: Each side is $90$ m

Radha and Mohan start from Q and R, at $8$ km/h and $10$ km/h respectively. When they first meet, they will have collectively travelled $270$ m (excluding the 90m of QR)

Let's take the ratios of their speed $=8:10=4:5$

So, Radha covers $=\frac{4}{4+5}\times270=\frac{4}{9}\times270=120$ m

and Mohan covers the remaining $150$ m.

Hence, they meet at PS, when Radha is 60m far from S, and Mohan is 30m from P.

Now, for their second meeting, they will both collectively cover $360$ m.

Taking ratios again, Radha will cover $=\frac{4}{9}\times360=160$ m and Mohan will cover the remaining $200$ m

So, they meet at QR, where Radha and Mohan are $10$ m from R (or $80$ m from Q).

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