Why Might a Math Solution Involve Doubling the Percentage Difference?

[tahmidbro]

Homework Statement

My answer does not match with the ones in book

Relevant Equations

N/A

See the question : https://www.thestudentroom.co.uk/att...hmentid=978958

The mark scheme/answer : https://www.thestudentroom.co.uk/att...hmentid=978956

I have got the answer to the vertical height gained = 1.355 m. No problem.

But not the value of the percentage difference. Their value : 23%, my value =( (1.355-1.2 )/1.35) x 100% = 11.48%

Well, I suspect that they are multiplying %D by 2, but why?

 

[jbriggs444]

If you read the question, you will find that you were asked to compare against 1.1, not against 1.2

Compare your answer with the 1.1 m calculated in the...

 

[Steve4Physics]

Homework Statement:: My answer does not match with the ones in book
Relevant Equations:: N/A

See the question : https://www.thestudentroom.co.uk/att...hmentid=978958

The mark scheme/answer : https://www.thestudentroom.co.uk/att...hmentid=978956

I have got the answer to the vertical height gained = 1.355 m. No problem.

But not the value of the percentage difference. Their value : 23%, my value =( (1.355-1.2 )/1.35) x 100% = 11.48%

Well, I suspect that they are multiplying %D by 2, but why?

Your first link says the calculated height is 1.1m, not 1.2m.
You are asked for the % difference relative to 1.1m, so you should divide (1.355 - 1.1) by 1.1

 

[tahmidbro]

Now I understand. Thank you!

 

[jbriggs444]

I have a minor quibble with the response given by @Steve4Physics. He points out quite correctly that if one is computing the percentage difference of 1.355 from 1.1 that one should divide the delta by 1.1.

However, the question at hand does not specify whether we should use the 1.1 or the 1.355 as the baseline.

calculate the percentage difference between the two answers

There is nothing in that request that elevates either of the two answers to the status of baseline. One could argue for the correctness of any of three possible answers to this ambiguous question.

1. $\frac{\text{high}-\text{low}}{\text{low}}$
2. $\frac{\text{low}-\text{high}}{\text{high}}$
3. $\frac{\text{high}-\text{low}}{\text{high}}$

 

[tahmidbro]

Sorry for forgetting to upload the 'worked example' along with the question
My bad :-d

 

[Steve4Physics]

There is nothing in that request that elevates either of the two answers to the status of baseline. One could argue for the correctness of any of three possible answers to this ambiguous question.

Agreed that the question isn't particularly well expressed, but the OP's first link explicitly says
"Compare your answer with the 1.1m calculated in the worked example..."
which implies 1.1m is the 'baseline'.

 

[jbriggs444]

Sorry for forgetting to upload the 'worked example' along with the question
My bad :-d

For future reference, it is much easier to quote sections of the problem if it is transcribed as text rather than attached as an image.