The diagram above shows the bar charts representing the number of vehicles manufactured by a company in January, February and March, 1992. (a) How many vehi...
Question 1 Report
The diagram above shows the bar charts representing the number of vehicles manufactured by a company in January, February and March, 1992.
(a) How many vehicles were produced in February?
(b) What fraction of the vehicles manufactured in February were cars?
(c) How many buses were produced altogether from January to March, 1992?
(d) What is the ratio in the lowest term of the number of lorries produced in February to that in March?
Answer Details
Read the height of every bar against the vertical scale, which is marked in steps of \(5\) vehicles. Match each shading to the key: fine dots are cars, solid black is lorries, diagonal cross-hatching is buses. Reading each of the three bars in each month group gives the table below.
| Month | Cars | Lorries | Buses | Monthly total |
|---|---|---|---|---|
| January | 10 | 15 | 20 | 45 |
| February | 40 | 25 | 30 | 95 |
| March | 5 | 35 | 50 | 90 |
The same data drawn to scale:
(a) Vehicles produced in February. Add the three February bars:
\[ 40 + 25 + 30 = 95 \text{ vehicles.} \]
(b) Fraction of February vehicles that were cars. Cars in February over the February total:
\[ \frac{40}{95} = \frac{8}{19}. \]
(c) Buses produced altogether, January to March. Add the three bus readings:
\[ 20 + 30 + 50 = 100 \text{ buses.} \]
(d) Ratio of lorries in February to lorries in March. The lorry bars read \(25\) and \(35\). Divide both by their highest common factor, \(5\):
\[ 25 : 35 = 5 : 7. \]
The key point when reading a grouped bar chart is to fix the scale first (each square here is \(5\) vehicles) and to match every bar to the correct shading in the key before adding. Miscounting the scale or reading the wrong shading is what leads to a wrong total such as treating February as \(75\) instead of \(95\).
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