Select the correct answerA man walking at a speed of 30kmph reaches from his house to office at 5pm. Next time at a speed of 60kmph reaches from his house to office at 2pm find the distance of his office from home?Options160km180km120km140km

To solve this problem, we first need to understand that the distance between the man's house and his office remains the same regardless of his speed.

1. Let's denote the distance between the house and the office as D (in km), the speed of the man as S (in km/h), and the time it takes him to reach the office as T (in hours).

2. From the problem, we know that when the man walks at a speed of 30 km/h, he reaches his office at 5 pm. We don't know when he starts, but this information is not necessary for our calculation.

3. We also know that when he walks at a speed of 60 km/h, he reaches his office at 2 pm. Again, we don't know when he starts, but we know that he arrives 3 hours earlier than when he walks at a speed of 30 km/h.

4. From this information, we can set up the following equation using the formula D = S * T:

   When the man walks at 30 km/h, D = 30T When the man walks at 60 km/h, D = 60(T - 3) (because he arrives 3 hours earlier)

5. Since the distance D remains the same, we can set the two equations equal to each other:

   30T = 60(T - 3)

6. Solving this equation for T, we get T = 6 hours. This is the time it takes the man to reach his office when he walks at a speed of 30 km/h.

7. Substituting T = 6 into the equation D = 30T, we get D = 30 * 6 = 180 km.

So, the distance between the man's house and his office is 180 km. Therefore, the correct answer is 180km.