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)?

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