Round 1 - Budget Challenge! Determining and Understanding Ratios
RATIOS
Determining Ratios
This basic formulation-determining the relationship between two numbers, known
as a ratio-is one of the central elements of quantitative analysis. Of course,
we encounter ratios all the time, in areas that have nothing to do with budgets
or budget analysis. "Seventy percent of those surveyed prefer Coca Cola to
Pepsi," claims the advertisement, while two out of three Americans are
overweight, lament public health officials. Similarly, we often want to know
the share of total spending that education or military spending consists of, or
how government spending compares to other parts of the economy. The basic
calculation is this:
Section ÷ Total = Share
Of course, ratios are often expressed in percentage terms. So if four out of 10
people support the liberal party, instead of saying 0.4 we say 40 percent, while
if their support is only four out of 100 people, we say that only four percent
support the liberals (and that some other party must have a lot more support!).
Keep in mind that ratios can exceed one hundred percent. If for instance,
military spending is slightly greater than education spending, we might say that
the military amounts to 110 percent of education spending
In the basic form, then, ratios are quite simple and common. There is, however,
an important point to keep in mind regarding these ratios that has confused many
people. Keep in mind that ratios are relationships between two numbers; thus
the ratio changes when either number changes. Consider the situation where
income taxes make up 40 percent of total revenue one year, and 50 percent the
next. It is often assumed, then, that income taxes must have grown during that
period. In fact, it is possible (if not necessarily likely) that income taxes
were stagnant or even fell, while revenue from the VAT, for instance, fell such
that income taxes made up a larger share of a smaller total. If total revenue,
for instance, fell from $100 million to $80 million, while the income tax
remained at $40 million, the income tax would have grown from 40 percent to 50
percent of total revenue. Income taxes grew relative to all other revenue, but
did not grow in absolute terms.
Exercises for understanding ratios
1. In an office, 25 staff members drink water during lunch, 20 others drink
fizzy drinks, and the remaining five staff members do not drink anything during
lunch. What are the different ways of expressing the lunchtime drinking habits
of the staff members using ratios?
2. Continuing from our previous example, in the following year, seven staff
members who used to drink water during lunch resign from their jobs. They are
replaced by two new staff members who drink fizzy drinks during lunch. Also,
five of the old staff members who used to prefer fizzy drinks during lunch have
stopped doing so and have instead switched to drinking water. What is the
percentage of staff members who now drink water, drink fizzy drinks, or who
don't drink at all during lunch?
3. The share of staff members who drink water during lunch has gone down from 25
staff members in the previous year to 23 staff members in the subsequent year.
However, the percentage of staff members who drink water has increased year over
year. Explain this?
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Question 1
ANSWER:
(i) Half of the staff members drink water during lunch.
(ii) Forty percent of staff members drink fizzy drinks during lunch.
(iii) Only one out of ten staff members does not drink anything during lunch.
(iv) The ratio of staff members who drink water, fizzy drinks, or nothing at all during
lunch is 5:4:1.
(v) There are four times as many staff members who drink fizzy drinks during lunch than
staff members who don’t drink at all during lunch.
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Question 2
ANSWER:
51.1 percent, 37.78 percent, and 11.1 percent.
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Question 3
ANSWER
Because, ratios are affected by changes in either number, and in this case even though the total staff members who drink water during lunch has gone down from the previous year, the total number of staff members has also gone down.
Thanks for participating in Round 1 of the Budget Challenge!