Ratio of speeds of two trains is 5 : 3. First train runs 350 km in 2 hrs. Then…

When two objects' speeds are in a given ratio, express each speed as that ratio's terms multiplied by a common variable (for example 5x and 3x for a 5 : 3 ratio). Using one known speed value lets you solve for that common variable, and from it the other speed. This is the standard technique for ratio-of-speeds problems, and it works because ratio equality is preserved under a common scale factor.

1. Compute the first train's speed: 350 km ÷ 2 hr = 175 km/hr.

2. Let the speeds of the first and second train be 5x and 3x respectively, matching the given ratio 5 : 3.

3. Since the first train's speed is 175 km/hr, 5x = 175, so x = 35.

4. The second train's speed = 3x = 3 × 35 = 105 km/hr.

Check: 175 : 105 simplifies to 5 : 3 (dividing both by 35), matching the given ratio — confirming the second train's speed is 105 km/hr.