Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increases by:

Options

A. `2/5`
B. `1/8`
C. `2/7`
D. `1/7`

Answer

To solve the problem step by step, let's denote the total cost of the rental car as \( C \).

### Step 1: Calculate the initial share of each person
When 8 people are sharing the cost equally, the share of each person is given by:
\[ \text{Initial Share} = \frac{C}{8} \]

### Step 2: Calculate the new share after one person withdraws
When one person withdraws, the remaining 7 people will share the same total cost \( C \). The new share for each of the remaining 7 people is:
\[ \text{New Share} = \frac{C}{7} \]

### Step 3: Calculate the increase in share
To find out how much the share of each person has increased, we need to subtract the initial share from the new share:
\[ \text{Increase in Share} = \text{New Share} - \text{Initial Share} \]
Substituting the values we calculated:
\[ \text{Increase in Share} = \frac{C}{7} - \frac{C}{8} \]

### Step 4: Find a common denominator and simplify
To subtract these fractions, we need a common denominator. The least common multiple of 7 and 8 is 56. Thus, we rewrite the fractions:
\[ \text{Increase in Share} = \frac{8C}{56} - \frac{7C}{56} = \frac{8C - 7C}{56} = \frac{C}{56} \]

### Step 5: Conclusion
The increase in the share of each of the remaining persons is:
\[ \text{Increase in Share} = \frac{C}{56} \]