Question

P and Q are 27 km away. Two trains with speed of 24
km/hr and 18 km/hr speed respectively start
simultaneously from P and Q and travel in the same
direction. They meet at a point R beyond Q. Distance
QR is??

(a) 126 km
(b) 81 km
(c) 48 km
(d) 36 km​

Answer 1

Answer

Option b) 81 km

$\rule{100}2$

Explanation

Refer the attachment for figure.

The train at P starts with velocity 24 km/h

The train at Q starts with velocity 18 km/h

PQ = 27 km

They meet at R beyond Q.

Let QR be x.

Then, distance travelled by Train at P

= PQ + QR

= 27 + x

And, distance travelled by Train at Q

= QR

= x

They would meet at same time.

Time taken by train P = (27 + x)/24

(Time = distance/speed)

And, time taken by train Q = x/18

Since they would meet at same time,

(27 + x)/24 = x/18

Cross multiplying,

18 × 27 + 18x = 24x

→ 24x - 18x = 18 × 27

→ 6x = 18 × 27

→ x = 18 × 27/6

→ x = 3 × 27

→ x = 81 km

→ QR = x = 81 km

Answer 2

AnswEr :

Refer to the Attachment For Image :

$\bold{Given} \begin{cases} \sf{Speed \: of \: Train \: P = 24 km/h} \\ \sf{Speed \: of \: Train \: Q = 18 km/h} \\ \sf{Distance\:b/w\: P \: and \: Q=27 km}\end{cases}$

Both Train P & Q meet at a point R beyond Q.

we need to find the Distance of QR.

$\large \boxed{ \sf{Distance = Speed \times Time}}$

Let the trains meet at t hour.

⇒ Train P - Train Q = Distance b/w them

⇒ (Speed × time) - (Speed × time) = 27

⇒ (24 × t) - (18 × t) = 27

⇒ 24t - 18t = 27

⇒ 6t = 27

⇒ t = $\sf\cancel\dfrac{27}{6}$

⇒ t = $\sf\dfrac{9}{2}\:hr$

_________________________________

• we will find the Distance of QR Now :

Train Q is Going with Speed 18 km/h and Time taken is $\sf\dfrac{9}{2}\:hr$, Distance will be :

⇒ Distance = Speed × Time

⇒ QR = $\sf\cancel{18}\times\dfrac{9}{\cancel2}$

⇒ QR = 9 × 9

⇒ QR = 81 km

⠀

∴ Distance of QR is [ b.] 81 Km