Question

A square field ABCD of side 90 m is so located that its diagonal AC is from north to south and the corner B is to the west of D. Muong and Thames start walking along the sides from B and C respectively in the clockwise and anticlockwise direction with speeds of 8 m/s and 10 m/s. Where shall they cross each other the second time?

• A. On AD at a distance of 30 m form A
• B. On BC at a distance of 10 from B
• C. On AD at a distance of 30 m from D
• D. On BC at a distance of 10 m from C

Answer 1

The correct option is D On BC at a distance of 10 m from C

Clearly, the arrangement is as shown in the adjoining diagram.
It is given that

Ram speed = 8 m/s
Thames's speed = 10 m/s

It is clearly visible from the above figure that to meet for the first time they have to cover a distance 270 m i.e three arms length of the field.

$BA+AD+CD=90+90+90=270m$

Since they are running in clockwise and anticlockwise direction respectively, they have to cover a distance of 360 m (i.e. 4 arms length of the field) for their second meeting from the first meeting point.

Thus, total distance to be covered for their second meeting
$=270+360=630m$

Time required $=\frac{630}{8+10}=\frac{630}{18}$
$=35$ seconds

Distance covered by Ram in clockwise direction in 35 seconds $=35\times 8=280m$

Distance covered by Thames in anticlockwise direction in 35 seconds $=35\times 10=350m$

Thus, Ram and Thames will meet on BC at a point 10 m form C and 80 m from B.