Aptitude - Simplification - Discussion

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.

Let the cost be 300 and the number of people initially be 6.
The share of one person =1/6.
ie the share is 300*(1/6)=50.
Now if one person leaves the new share would be1/5.
ie 300*(1/5)=60.
So the share per person increased by 10.

Now according to the answer provided above the share will increase by 1/5 in this equation. which should then be equal to 10..lets try this,
300(1/5)=60 which by the way is the total amount every person has to pay.

The real increment how ever is,
1/5-1/6=1/30.

Let us check this out now,
300(1/30)=10And we know this is the right answer.

So in the real question, it will be 1/7-1/8=1/56.

@All.

Here is the solution;

Suppose the car cost 56.

So, divided into equal 8 parts, each one gets 7.

If one person pulls out, the same amount is divided into 7 parts, each one gets 8.

So, if the question is how much each person shares increased.

The answer is, it increased by 1 right? because it was 7 and it became 8 for each person. You don't need to divide it by 7 (which is the original share before one person withdrawing). Because the question it asks for the increase in each person's share, which is the difference between the share before and after the withdrawal for each person.

Assume the cost of the car is C.

The contribution of each of the initial 8 individuals is c/8.

Now because one drops out, his contribution of c/8 is to be shared equally by the remaining 7 individuals.

Mathematically it is 1/7 (c/8) =c/56. NOTE THIS IS THE AMOUNT THAT IS BEARED IN EXCESS BY EACH PERSON.

Now the question asks share of each of the remaining person increases by? Here what refers to the fraction of additional payment they have to make.

Which is c/8 + c/56 = c/8 (1+1/7).

Hence the increase is 1/7. Hope this helps.

It's easy. Think of it theoretically than mathematically.

8 people are going to share their money for one car.So each contributes 1/8 of the amount of the car,that is;

1/8+1/8+1/8+1/8+1/8+1/8+1/8+1/8 = 8/8=1(Car's amount).

If one person withdraws then 7 people share their money for that car. So each contributes 1/7.
Adding up 1/7 seven times gives 1(Car's amount).

1/7 is greater than 1/8 (1/7=14% and 1/8=12%).

So when 7 people instead of 8 share the amount, each individual share is increased from 1/8 --->1/7.

The Answer is 1/7.

Initially share is 1/8 (since 8 people are sharing) so it means there are eight of 1/8).

Then one back off, therefore only seven 1/8 is left, so the eighth one has to be distributed equally among seven of those who did not back off, so 1/8 x7 =1/56 (which is the extra share). So now each of the eight-person share increase by 1/8 + 1/56 = 15/56.

Therefore increased in share is.

New share - old share.

Therefore, 1 15/56 - 1/8 = 1/7.

The easiest way to understand :
Initially, 8 people were to share the cab but since 1 person opted out, 7 had to share the bill.
Let's take the LCM of 8 & 7 which equals to 56.
So if 8 were to share, the cost per head would have been Rs. 7 per person
but now the cost per head = 56/7 = Rs. 8.

The question is by how much did the share increase? or to put it here, how much is the increase from 7 to 8?
its (8-7)/7 = 1/7 (Ans).

It is clearly asked , "increased by "
(not increase in share , otherwise answer would be 1/56)
This means increment w.r.t initial share.

So,
Initial share of one person =1/8,
Nd now after withdrawal of one person, new share = 1/7,
so, increment =(1/7 - 1/8)=1/56.

So, share increased by,
=(increment in share /initial share)
=1/56÷1/8 = 1/7 answer.

Hope you all will get the point.

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.

Assume the price of the car be 100Rs.
By quuestion, Eight people will equally share the rental of the car But one leaves the deal so
Case beforehand
100/8= 12.5rs to be paid by each

One leaves the deal
100/7 = 14.285rs
Increase in price to be paid equally by all 7
14.285-12.5 = 1.785

Now how many times of the original price is contained in the increment value
1.785/12.5 = 1/7.