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.

Good explanation, Thanks @Prank.

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.

Let total cost beared by 8 be 64.
8-64
1 people have to bear 8 rupee
When one people withdrew
64÷7 = 9.243.
Additional cost = 9.243-8 =1.143.

Let's check the answer from the given option by converting it in %.
(1÷7)*100=14.3%.

And, as we get;
(1.143÷8)*100 = 14.3%.
Hence proved that 1/7 is correct.

@All.

Answer is 1/7 when it's is said that "increased to" as 1/56 + 1/8 =1/7.

But according to the question, "increased by" so answer will be 1/8 as (1/7-1/56).

Correct me, if I am wrong.

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)

If car rate is x and initial contribution is why then,

Increased contribution of each person is x/56 or y/7.

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.

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.