Reshmi and Sulogna started moving at the same time from the same place for a…

For a fixed distance, time and speed are inversely related (Time = Distance ÷ Speed). So if one traveller's speed is a certain fraction of another traveller's speed, that traveller's time is the reciprocal of that fraction times the other's time.

1. Let the time Reshmi takes to reach the destination be x hours.

2. Sulogna starts at the same time but reaches 5 hours after Reshmi, so Sulogna's time = (x + 5) hours.

3. Sulogna walks at ¾ of Reshmi's speed, so the speed ratio Sulogna : Reshmi = 3 : 4.

4. Since they cover the same distance, the time ratio is the reciprocal of the speed ratio: Reshmi's time : Sulogna's time = 3 : 4, i.e. Reshmi's time = ¾ × Sulogna's time.

5. This gives the equation: x = (x + 5) × ¾.

6. Multiply both sides by 4: 4x = 3(x + 5) = 3x + 15.

7. Solve for x: 4x − 3x = 15 ⇒ x = 15.

8. So Reshmi's time = 15 hours, and Sulogna's time = x + 5 = 15 + 5 = 20 hours.

Check: Sulogna's speed ÷ Reshmi's speed should equal Reshmi's time ÷ Sulogna's time = 15 ÷ 20 = ¾, which matches the given speed ratio — confirming the answer.

So Sulogna reaches the destination in 20 hours.