Question

Two trains, one from station A to station B and the other from B to A start simultaneously. After meeting, the trains reach their destinations after 9 h and 16 h respectively. The ratio of their speeds is (a) 2:3 (b) 4:3 (c) 6:7 (d) 9:16.​

Answer 1

Answer:

4 : 3

Step by Step Explanation:

Let, the total distance between A and B be l km.

Trains meet at a distance of x km from station A, i.e., (l-x) km from B.

Also,

Let v1 be the speed of train starting from A and v2 be the speed of train starting from B.

Now,

$v1 = \frac{x}{t} = \frac{(l - x)}{9} \\ \frac{x}{(l - x)} = \frac{t}{9}$

And,

$v2 = \frac{(l - x)}{t} = \frac{x}{16} \\ \frac{x}{(l - x)} = \frac{16}{t}$

Equating both we get,

$\frac{t}{9} = \frac{16}{t} \\ {t}^{2} = 16 \times 9 \\ t = 12$

Then,

$v1 = \frac{x}{t} = \frac{x}{12}$

and,

$v2 = \frac{x}{16}$

Therefore,

$Required \: Ratio = \frac{ \frac{x}{12} }{ \frac{x}{16} } = \frac{16x}{12x} \\ = 4:3$

Hope It Helps :)