Question

two train one from Ghaziabad and another from Aligarh start simultaneously after crossing each other they reach the destination after 16 hour and 25 hour respectively find the ratio of their speeds.​

Answer 1

Answer:

5:4

Step-by-step explanation:

Let us assume that the distance between Ghaziabad and Aligarh is d and p and q are the speed of the trains from Ghaziabad and Aligarh respectively.

So, they will meet with each other after $\frac{d}{p+q}$ hr. from the starting time.

Hence, total time taken by the train from Ghaziabad to cover d distance will be $[\frac{d}{p+q}+16] hours$

So, $\frac{d}{\frac{d}{p+q}+16 }=p$

⇒$d=\frac{dp}{p+q}+16p$

⇒$d(\frac{q}{p+q} )=16p$ ....... (1)

Again, total time taken by the train from Aligarh to cover d distance will be $[\frac{d}{p+q}+25] hours$

So, $\frac{d}{\frac{d}{p+q}+25 }=q$

⇒$d=\frac{dq}{p+q}+16q$

⇒$d(\frac{p}{p+q} )=16q$ ....... (2)

Dividing equatio (1) with equation(2) we get,

$\frac{q}{p} =\frac{16p}{25q}$

⇒$\frac{p^{2} }{q^{2} } =\frac{25}{16}$

⇒$\frac{p}{q} =\frac{5}{4}$

Therefore, the ratio of the speed of the two trains will be 5:4. (Answer)