Question

A train travels a distance of 300 km at constant speed of
the train is by increased by 5km an hour, the journey
would have taken 2 hours less. Find the original speed of the train
​

Answer 1

Answer:

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Answer 2

$\large \star \: \: \underline{ \underline{ \red{ \tt{given : }}}}$

$\\ \large \tt \: \: \: \: \: \: \: \rightarrow \: distance = 300km \\ \\ \large \tt \: \: \: \: \: \rightarrow \: increased \: \: speed = 5km\\ \\ \large \tt \: \: \: \: \: \: \: \rightarrow \: time = 2hr \: \: less$

$\large \tt \bull \: let \: \: constant \: \: speed \: \: of \: \: train \\ \large \: \: \: \tt \: \: = \green{ x \: \: km / hr}$

$\large \tt: \implies time \: \: tken \: \: to \: \: cover \: \: 300km \\ \\ \large \tt \: \: \: \: = \frac{300}{x} hrs$

$\large \tt: \rightarrow \: seed \: \: increased \: \: by \: \: 5km/h \\ \\ \large \tt \: \: \: \: = \frac{300}{x + 5} hrs$

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$\:$

➪ It is given that the time to cover 300km is reduced by 2 hours

$\\ \large \tt \therefore \: \: \frac{300}{x} - \frac{300}{x + 5} = 2$

$\large : \implies \tt \dfrac{300(x + 5) - 300x}{x(x + 5)} = 2 \\ \\ \\ \large : \implies \tt 2 {x}^{2} + 10x = 1500 \\ \\ \large : \implies \tt {x}^{2} + 5x - 750= 0 \\ \\ \large \rm \underline{\underline{splitting \: \: the \: \: middle \: \: term : }} \\ \\ \large : \implies \tt {x}^{2} + 30x - 25x - 750= 0 \\ \\ \large : \implies \tt (x + 3)(x - 25) = 0$

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$\large \boxed{\rm \therefore \underline{ \:x = 25 \: \: or \: \: x = - 30}}$

Since, x cannot be negative

• therefore, x = 25km/h

Hence,

• Original speed of train = 25km/h