[11 a.m.] The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travel toward

The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travel towards B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at 75 Km/hr. At what time will they meet?

10.30 a.m.

10 a.m.

12 noon

11 a.m.

Explanation:

Assume that they meet $ x $ hours after 8 a.m.

Then, train1,starting from A , travelling towards B, travels x hours till the trains meet

$\Rightarrow$ Distance travelled by train1 in x hours = Speed $\times$ Time = 60$x$

Then, train2, starting from B , travelling towards A, travels $\left(x-1\right)$ hours till the trains meet

$\Rightarrow$ Distance travelled by train2 in $\left(x-1\right)$ hours = Speed $\times$ Time = 75$\left(x-1\right)$

Total distance travelled = Distance travelled by train1 + Distance travelled by train2

=> 330 = 60$x$ + 75$\left(x-1\right)$

=> 12$x$ + 15$\left(x-1\right)$ = 66

=> 12$x$ + 15$x$ - 15 = 66

=> 27$x$ = 66 + 15 = 81

=> 3$x$ = 9

=> $x$ = 3

Hence the trains meet 3 hours after 8 a.m., i.e. at 11 a.m.

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