Trains Boats and Streams Practice Test 1 with solutions

Let the distance in stations A and B is x kms
Speed = y kmph
Time = 45 minutes = $\frac{45}{10}$ = $\frac{3}{4}$ hrs
New speed of the train = (y - 5) kmph
Time = 48 minutes
= $\frac{48}{60}$ = $\frac{4}{5}$ hrs
= $\frac{3}{4}$ = $\frac{\mathit{x}}{\mathit{y}}$
⇒ x = $\frac{3}{4}\mathit{y}$ ... (i)
and $\frac{4}{5}$ = $\frac{\mathit{x}}{-5}$
⇒ x = $-5\frac{4}{5}$
x = $\frac{4}{5}\mathit{y}-4$ ... (ii)
From equation (i) and (ii) we get,
$\frac{3}{4}\mathit{y}$ = $\frac{4}{5}\mathit{y}-4$
4 = $\frac{4}{5}\mathit{y}-\frac{3}{4}\mathit{y}$
4 = $\frac{16\mathit{y}-15\mathit{y}}{20}$
4 = $\frac{\mathit{y}}{20}$
y = 80 kmph
Distance between station A and B is
x = $\frac{3}{4}\times 80$ = 60 kms