You are Here: Home >< Maths

# Help in Maths Question watch

1. Hello, I need help in a Maths question.

P increased by 25% is equal to Q decreased by 30%. Work out P as a percentage of Q.

I am not sure how to work it out, maybe ratios are involved? Thank you
2. (Original post by salex413)
Hello, I need help in a Maths question.

P increased by 25% is equal to Q decreased by 30%. Work out P as a percentage of Q.

I am not sure how to work it out, maybe ratios are involved? Thank you
Can you write P increased by 25% algebraically?

In the future, the place for maths questions is F38 (the Maths Forum).
3. P + 0.25P = Q - 0.3Q ----- Write the problem out algebraically
P (1+ 0.25) = Q (1 - 0.3) ---------- factor out P and Q
P (1.25) = Q (0.7) ------ do the in bracket sums/subtraction
P = Q (0.7)/(1.25) -------- rearrange for P
P = Q0.56 ------- answer in decimal
Therefore P = 56%Q ----- answer as a %

Always test to confirm solution. For example lets assume P to be 4. If P is four then P +0.25P should be 5.
Since P= 56%Q then Q should be 7.14.
If we put 7.14 into Q-0.3Q we should also get 5.
7.14 - 0.3(7.14) = 7.14 - 2.14 = 5.
Therefore solution is correct.
4. 1.25P = 0.7Q

divide by 1.25

P = 0.56Q

thus P = 56% of Q
5. 25% increase of P can be written as 1.25 x P
30% decrease in Q can be written as 0.7 x Q

These are equal to each other so:
1.25P=0.7Q

Now isolate P (by dividing by 1.25) as you are working out P in terms of Q:
P= 0.7Q / 1.25
Simplified to-> P=0.56Q
This means that P is equal to 56% of Q.
6. (Original post by frankielogue)
...
Please don't post full solutions. Just give hints that nudge people towards the answer.
7. (Original post by srata)
...
Please don't post full solutions. Just give hints that nudge people towards the answer.
8. (Original post by Mr M)
Please don't post full solutions. Just give hints that nudge people towards the answer.
sorry!
9. (Original post by Mr Optimist)
P + 0.25P = Q - 0.3Q ----- Write the problem out algebraically
P (1+ 0.25) = Q (1 - 0.3) ---------- factor out P and Q
P (1.25) = Q (0.7) ------ do the in bracket sums/subtraction
P = Q (0.7)/(1.25) -------- rearrange for P
P = Q0.56 ------- answer in decimal
Therefore P = 56%Q ----- answer as a %

Always test to confirm solution. For example lets assume P to be 4. If P is four then P +0.25P should be 5.
Since P= 56%Q then Q should be 7.14.
If we put 7.14 into Q-0.3Q we should also get 5.
7.14 - 0.3(7.14) = 7.14 - 2.14 = 5.
Therefore solution is correct.
Thank you so much! I understand it and your working out is very clear and understandable. Thanks a bunch
10. (Original post by frankielogue)
1.25P = 0.7Q

divide by 1.25

P = 0.56Q

thus P = 56% of Q
Thank you so much! This is very helpful
11. (Original post by srata)
25% increase of P can be written as 1.25 x P
30% decrease in Q can be written as 0.7 x Q

These are equal to each other so:
1.25P=0.7Q

Now isolate P (by dividing by 1.25) as you are working out P in terms of Q:
P= 0.7Q / 1.25
Simplified to-> P=0.56Q
This means that P is equal to 56% of Q.
Thank you for your help and working out too! Thanks a lot

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: January 15, 2017
Today on TSR

### Flight U-turns after...

human heart discovery

### University open days

• University of Lincoln
Mini Open Day at the Brayford Campus Undergraduate
Wed, 19 Dec '18
• University of East Anglia
Fri, 4 Jan '19
• Bournemouth University
Wed, 9 Jan '19
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams