A train x running at 74 km/h crosses another train y running at 52 km/h in the opposite direction in 12 seconds. If the length of y is two-thirds that of x, then what is the length of y (in m)?

Answer: Option C

According to question,
$$\begin{array}{rl}& \frac{x+y}{\left(74+52\right)\frac{\text{km}}{\text{hr}}}=12\\ & x+y=12\times 126\times \frac{5}{18}\\ & x+y=420\text{ m }\text{. }\text{. }\text{. }\text{. }\text{. }\text{. }\left(\text{i}\right)\end{array}$$
y = 3a + 2a = 5a
x = 3a
So, from equation (i)
5a = 420
a = 84
Hence length of train y = 2 × 84 = 168