A cyclist, after cycling a distance of 70 km on the second day, find that the ratio of distance covered by him on the first two days is `4:5`. If he travels a distance of 42km On the third day, then the ratio of distance travelled on the third day and the first days is

Options

A. `4:3`
B. `3:2`
C. `3:4`
D. `2:3`

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the given information
The cyclist cycled 70 km on the second day. The ratio of the distances covered on the first two days is given as 4:5.

### Step 2: Set up the equations based on the ratio
Let the distance covered on the first day be \(4x\) and the distance covered on the second day be \(5x\). According to the problem, the distance covered on the second day is 70 km. Therefore, we can set up the equation:
\[ 5x = 70 \]

### Step 3: Solve for \(x\)
To find \(x\), we divide both sides of the equation by 5:
\[ x = \frac{70}{5} = 14 \]

### Step 4: Calculate the distance covered on the first day
Now that we have \(x\), we can find the distance covered on the first day:
\[ \text{Distance on the first day} = 4x = 4 \times 14 = 56 \text{ km} \]

### Step 5: Distance covered on the third day
The cyclist travels 42 km on the third day.

### Step 6: Find the ratio of the distance traveled on the third day to the first day
Now we need to find the ratio of the distance traveled on the third day (42 km) to the distance traveled on the first day (56 km):
\[ \text{Ratio} = \frac{\text{Distance on third day}}{\text{Distance on first day}} = \frac{42}{56} \]

### Step 7: Simplify the ratio
To simplify the ratio:
\[ \frac{42}{56} = \frac{42 \div 14}{56 \div 14} = \frac{3}{4} \]

### Final Answer
The ratio of the distance traveled on the third day to the distance traveled on the first day is \(3:4\).

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