Walking at 2/3 of his speed, Ramesh is 24 minutes late in reaching his office. What is the usual time taken by him to reach office?

Let's solve this step by step:

Step 1: Let's assume the usual speed of Ramesh is S km/hr and the usual time taken by him to reach office is T hours.

Step 2: According to the problem, when Ramesh walks at 2/3 of his usual speed, he is 24 minutes late. This means he takes T + 24/60 hours to reach office at this slower speed.

Step 3: We know that Distance = Speed x Time. The distance to the office remains the same, regardless of Ramesh's speed. So, we can set up the following equation:

S*T = (2/3)S(T + 24/60)

Step 4: Simplify the equation. The S on both sides will cancel out:

T = (2/3)*(T + 24/60)

Step 5: Solve the equation for T. First, distribute the 2/3:

T = 2/3T + 2/324/60

Step 6: Subtract 2/3*T from both sides to isolate T on one side:

1/3T = 2/324/60

Step 7: Multiply both sides by 3 to solve for T:

T = 2*24/60

Step 8: Simplify to find the value of T:

T = 48/60 = 0.8 hours

So, the usual time taken by Ramesh to reach his office is 0.8 hours or 48 minutes.