Hi, Reymond

Can you help provide solution ?

Alla is 2/3 as old as Bebe. In 15 years' time, alla will be 5/6 of Bebe's age How old is alla now?

Hi Daryl,

This is a Constant Difference type of question.

The difference in age between Alla and Bebe will remain constant no matter how many years in the future or the past. Therefore, we can compare the difference in units now against the difference in units in 15 years time.

• If the difference in units is the same, we can solve the question.
• If the difference in units is different we need to make the difference the same using common multiples.

You can refer to Chapter 2.8 of the P5 +hinkingMath book on fractions for more questions.


First using units ...




Now using Models

Thanks Chris

It is rather hard for me to digest or fully appreciated the logic behind your approach which I am sure is perfectly correct. I think I will need some time to digest it. Iis there a easier approach?

Meanwhile, here is another one.

Leon's age is 4/9 of his grandfather's. His grandfather will be 65 years old in 2 years' time. How many years' agao was Leon's age 2/7 of his grandfather's?

Ok Chris,

I understood you logic and approach. But, what if the difference is not the same how would your approach be.

Hi Darly, that entirely depends on the situation. The reason we use this is approach is purely for the reason that the two items (in this case people) always have a constant difference. We see this quite often in Age questions. Another example would be when 3 adults and 3 kids got off the bus. If you search this forum for constant difference, I suspect you will find at least 10-15 similar questions rather from this style to some rather complex ones that all follow the same approach.

If the change was not consistent, then we need to ask ourselves what has changed and then apply the appropriate strategy. Eg. Only one item changed; both items changed by a different amount; no change but there are values and quantities.

A very similar question however "they" have chosen to give the information slightly differently. Regards, our objective is still the same since there is a Constant Difference - that being compare the difference between the two points in time (before vs after) to ensure the difference in units is the same. Once it is the 'math' is quite straight forward.

Here is a list of Constant Difference questions that can be found in the forum.

Involving Money
- www.onsponge.com/forum/35-thinkingmathon...oblem-sums.html#1488
- www.onsponge.com/forum/35-thinkingmathon...5-p5-maths.html#1205

Using Ratios
- www.onsponge.com/forum/35-thinkingmathon...oblem-sums.html#1385

Using Geometry
- www.onsponge.com/forum/35-thinkingmathon...-difference.html#649
- www.onsponge.com/forum/35-thinkingmathon...-difference.html#627

Others
- www.onsponge.com/index.php?option=com_ku...61&catid=35#1361
- www.onsponge.com/index.php?option=com_ku...07&catid=35#1308
- www.onsponge.com/forum/35-thinkingmathon...rence-ratio.html#914
- www.onsponge.com/index.php?option=com_ku...274&catid=35#274



More Difficult
- www.onsponge.com/index.php?option=com_ku...14&catid=35#1114

Hi, Chris

Thank you kindly for all your help. Will take time to go through.

Thanks again.