When Gopal walks from A to B and returns from B to A on cycle, it takes him 46 minutes. By walking both ways, it takes him 75 minutes. If the rides cycle both ways what will be the total time (in minutes)?

Options

A. A) 19
B. B) 17
C. C) 23
D. D) 15

Answer

To solve the problem step by step, let's define the variables and equations based on the information provided.

### Step 1: Define Variables
Let:
- \( W \) = time taken to walk from A to B (in minutes)
- \( C \) = time taken to cycle from B to A (in minutes)

### Step 2: Set Up the Equations
From the problem, we have two scenarios:
1. When Gopal walks from A to B and returns from B to A on a cycle, the total time is 46 minutes:
\[ W + C = 46 \quad \text{(Equation 1)} \]

2. When Gopal walks both ways, the total time is 75 minutes:
\[ 2W = 75 \quad \text{(Equation 2)} \]

### Step 3: Solve Equation 2 for W
From Equation 2:
\[ W = \frac{75}{2} = 37.5 \text{ minutes} \]

### Step 4: Substitute W into Equation 1
Now substitute \( W \) into Equation 1:
\[ 37.5 + C = 46 \]

### Step 5: Solve for C
Now, solve for \( C \):
\[ C = 46 - 37.5 = 8.5 \text{ minutes} \]

### Step 6: Calculate Time for Cycling Both Ways
If Gopal rides the cycle both ways, the total time will be:
\[ 2C = 2 \times 8.5 = 17 \text{ minutes} \]

### Final Answer
Thus, if Gopal rides the cycle both ways, the total time taken will be **17 minutes**.

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