**Question**

**Introduction**

This is a
question on percentages. Percentages are
in themselves also units. One percent
(1%) simply means

^{1}/_{100}. And we can use units (shown circled in the diagrams below) in which each unit is^{1}/_{100}or 1% of some whole.
It is
useful to think of increases and decreases as multiplying by some
percentage. For example, a decrease by
20% means multiplying by 100% – 20%
i.e. 80%. After all, if you work out 100%
of something and subtract
20% of the same thing, you will end up with 80% of
that thing. It is much easier to think
of it that way. Likewise, an increase
of 45%
means multiplication by 100% +
45% = 145%.

**Solution**

From the information given in the question, we can set up a diagram like
this. I use circles to envelop the
percentage units.

We can work out the units in the “after”
situation (one year later):-

40 × 80% =
40 ×

^{4}/_{5}= 32
60 × 145% = 60 ×

^{29}/_{20}= 87
The new total is 119%
or 119 circle units. The net increase is 19%
or 19 circle units, which we know
is equivalent to 228. Once we got this part, we can work out 1
circle unit and then 20 circle units, which is the difference
between the number of male and female members.
[Remember the check that you are answering the question that was asked.]

**Ans:**240

**Summary**

We have
used a diagram in the form of a ratio-units model [H02]. The ratio unit used in this example happens
to be the same as a percentage. Be
careful that other questions may involve different kinds of units with
different bases for their percentages.
In other words, in other questions, the “100%” may stand for different
things. In the diagram, we have used the
before-after concept [H06]. Increases or decreases in percentages may be
re-stated as multiplications by the appropriate percentages, which, in turn,
may be thought of as multiplications by fractions [H09]. It is a good idea to be able to inter-convert
between fractions and percentages. By
comparison, we found the link between 19
units (or 19%) and 228 [H11]. Having solved this part of the problem, we
are able to answer the original question as asked.

H02. Use a
diagram / model

H06. Use
before-after concept

H09. Restate
the problem in another way

H11. Solve part
of the problem

**Suitable Levels**

*****Primary School Mathematics

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