Question

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 rental of the car, then the share each of the remaining persons is increased by ______ of the original share.
a)\[\dfrac{1}{9}\]
b) \[\dfrac{1}{8}\]
c) \[\dfrac{1}{7}\]
d) \[\dfrac{7}{8}\]

Answer 1

Hint: Let us assume that the total price of the car is Rs. x. Initially, we have a total number of people is 8. So, each person shares the cost of the car at $Rs.\dfrac{x}{8}$. Later we have a total number of people as 7. So, find the share of cost each person shares. Now, subtract the initial share from the final share to find the value of the share increased. Now, we need to find the fraction of share increased. So, divide the share increased from the initial share.

Complete step-by-step solution:
As we have assumed that the total price of the car is Rs. x.
We have an initial number of people = 8
So, the initial share of each person is: $Rs.\dfrac{x}{8}............(1)$
Now, we have an initial number of people = 7
So, the initial share of each person is: $Rs.\dfrac{x}{7}............(2)$
Now, subtract equation (1) from equation (2), to find the share increased for each person. We get:
$\begin{align}
  & =\dfrac{x}{7}-\dfrac{x}{8} \\
 & =Rs.\dfrac{x}{56}............(3) \\
\end{align}$
Now, we need to find the fraction of the share increased.
So, divide equation (3) by equation (1), we get:
$\begin{align}
  & =\dfrac{\dfrac{x}{56}}{\dfrac{x}{8}} \\
 & =\dfrac{8}{56} \\
 & =\dfrac{1}{7} \\
\end{align}$
Hence, option (c) is the correct answer.

Note: While finding the increased share, we need to subtract the initial share from the final share. Do not assume that the final share is the increased share. Also, it is asked to find the ratio of the increased share of the original share. So, do not forget to divide the increased share by the original share.