Aptitude - Simplification - Discussion

@All.

Here is the calculation;
Assume the cost of the car be x. And equally distributed in 8 people, means 1 person has to pay x/8.
Now 1 person is back off, which means there are a total of 7 people remaining.
Now they've to pay the cost equally and it'll be x/7.

@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.

Rate of car : 8x.
Each one contributed: x.
If one person withdraws, 7x will be left. To make it 8x again, each one gives x/7.
x+x/7. 1/7 increased.

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.

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.

Good explanation, Thanks @Prank.

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.

1/7 is correct.

We have to find the ratio of increase in share.
Ratio = increase in share / original share = (1/56) / (1/8) = 1/7.
7 people will have to share 1/56 per person more than before.
The ratio of increase in share = 1/7 (Ans)

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.