Aptitude - Simplification - Discussion

In this question, they asked for how much each person's cost is increased by and not the ratio of the increase.

So according to the question, the correct answer should be 1/56.

1/56 is total increment. That should be divided among 7 people then why 1/8?

Let the cost of the car be c.
Let each share be x.

Since 8 people are sharing equally c = 8x.

But one person withdraws from arrangement so now let each share be y,

So c will become as 7y.

Since in both cases, the cost is same we can write 8x = 7y. -----> equation 1.

From equation 1.

7y = 8x.

y = (8/7) * x.

(8/7) * x can be written as (1 + 1/7) * x.

So, increase in share value is 1/7.

Let's say that the cost of the car is Rs 56.

Share of 1 person = 56/8 = Rs 7.

Share of 1 person after leaving = 56/7 = Rs 8.

Cost increased = 8-7 = Rs 1.

Required fraction = 1/7.

zhey folks,
zeasy explanation for you:

Lets assume the Cab charges Rs. 560 ( multiple of 8 and 7).
So, per head cost shared initially = 560/8 = Rs. 70.

Now, in absence of one person, total person to share cab cost = 7.
Then share per head = 560/7 = Rs. 80.

Extra amount to be paid by each person = 80-70 = Rs. 10.
Therefore, ratio of extra amount paid = 10/70 = 1/7.

Let us assume the rent of the car is 80 Rs.

The rent is divided among 8 people then the share of each person is 10.

1 person is withdrawn the one person cost i.e 10Rs is divided among 7 people.
The divided amount is 10/7.

Hence all 7 persons get equal % of divided amount.
Hence the % is 10/7*80 = 1/7.

Let us take price of the car is Rs. 8.

It can share 8 people by 8/8rp each i.e 1 rupee.

But 1 person is withdrawn so now it can shares 7 people by 8/7 rupees.

So the increment is 1-8/7 = 1/7.

Hope you understand now :).

It is given that share would be divided among remaining person so why 1/8 is divided, it should be 1/7 can anyone clarify?

Note: increased by..

If the question is: 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 "increased by":

Answer would be 1/56 as explained above by others.

But if the question is "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:

("increased is" omitted)

Answer would be 1/7.

"then the share of EACH of the REMAINING persons increased by" so why the total increment of 1/56 is divided by the original share of one person? according to me it should be divided by new share of one person since question asking "EACH of the REMAINING persons ". Then the answer is 1/8.

If I have misunderstood the question or I'm wrong please correct me!