JIPMAT 2024 (LR) - 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 ? | PYQs + Solutions

JIPMAT 2024

Logical Reasoning

Directions

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 ?

PS

at a distance of

30 \mathrm{~m}

from

P

Q R

at a distance of

10 \mathrm{~m}

from

Q

PS

at a distance of

30 \mathrm{~m}

from

\mathrm{S}

QR

at a distance of

10 \mathrm{~m}

from

\mathrm{R}

Correct Option: 4

Note: Each side is

90

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

and Mohan covers the remaining

150

\newline

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

Taking ratios again, Radha will cover

=\frac{4}{9}\times360=160

m and Mohan will cover the remaining

200

So, they meet at QR, where Radha and Mohan are

10

m from R (or

80

m from Q).