The ratio of speeds at which Anil and Mukesh walk is 3 : 4. Anil takes 30 minutes more than the time taken by Mukesh in reaching the destination.
If Anil drives the car at twice the speed of his walking then the time required to reach his destination by car is :

Options

A. 45 min
B. 60 min
C. 1.5 h
D. 1 h 20 min

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the ratio of speeds
The ratio of speeds of Anil and Mukesh is given as 3:4. This means if Anil's speed is 3x, then Mukesh's speed is 4x for some value of x.

**Hint:** Remember that the ratio of speeds can help us find the ratio of times taken to cover the same distance.

### Step 2: Set up the relationship between time and speed
Since distance is constant for both Anil and Mukesh, we can use the relationship that speed is inversely proportional to time. Therefore, the ratio of their times will be the inverse of the ratio of their speeds.

If Anil takes time T_A and Mukesh takes time T_M, we can write:
\[ \frac{T_A}{T_M} = \frac{4}{3} \]

**Hint:** Inverse ratios are key when dealing with constant distances.

### Step 3: Express the time taken by Anil and Mukesh
Let’s denote the time taken by Mukesh as T_M. Then, according to the ratio, Anil's time T_A can be expressed as:
\[ T_A = \frac{4}{3} T_M \]

According to the problem, Anil takes 30 minutes more than Mukesh:
\[ T_A = T_M + 30 \]

**Hint:** Set up equations based on the relationships given in the problem.

### Step 4: Solve for T_M
Now we can set the two expressions for T_A equal to each other:
\[ \frac{4}{3} T_M = T_M + 30 \]

To eliminate the fraction, multiply the entire equation by 3:
\[ 4T_M = 3T_M + 90 \]

Now, isolate T_M:
\[ 4T_M - 3T_M = 90 \implies T_M = 90 \text{ minutes} \]

**Hint:** Isolate the variable to find the time taken by Mukesh.

### Step 5: Calculate the time taken by Anil
Now that we have T_M, we can find T_A:
\[ T_A = T_M + 30 = 90 + 30 = 120 \text{ minutes} \]

**Hint:** Use the value of T_M to find T_A.

### Step 6: Determine Anil's walking speed
Since Anil’s speed is 3x, we need to find the distance. The distance can be expressed as:
\[ \text{Distance} = \text{Speed} \times \text{Time} = 3x \times 120 \]

**Hint:** Remember that distance remains constant for both modes of travel.

### Step 7: Calculate the driving speed
Anil drives at twice his walking speed:
\[ \text{Driving Speed} = 2 \times 3x = 6x \]

**Hint:** Driving speed is directly related to walking speed.

### Step 8: Find the time taken to reach the destination by car
Using the distance calculated earlier:
\[ \text{Distance} = 3x \times 120 \]
We can set up the equation for time taken while driving (T_C):
\[ T_C = \frac{\text{Distance}}{\text{Driving Speed}} = \frac{3x \times 120}{6x} = \frac{120}{2} = 60 \text{ minutes} \]

**Hint:** Use the formula for time, which is distance divided by speed.

### Final Answer
The time required to reach the destination by car is **60 minutes**.

---