The line graph shows the profit percentage of two companies, X and Y, over the years. Profit % = [(Income - Expenditure) / Expenditure] * 100. Study the graph and answer the questions that follow.
If the income of both companies in 2020 was equal, what was the ratio of their expenditures (X:Y)?
Answer: B
Let the equal income be I. Let expenditures be E_X and E_Y.
For X in 2020, Profit=50%. So, I = E_X(1+0.50) = 1.5 E_X.
For Y in 2020, Profit=55%. So, I = E_Y(1+0.55) = 1.55 E_Y.
Therefore, 1.5 E_X = 1.55 E_Y.
The ratio E_X / E_Y = 1.55 / 1.5 = 155 / 150 = 31 / 30.
The ratio is 31:30.
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The table represents the demand and production (in thousands of tonnes) of a product for 2 companies A and B.
| Company | Demand | Production |
|---|---|---|
| A | 6000 | 5000 |
| B | 5500 | 6000 |
The demand for the product of company A is what per cent more than its production?
Answer: B
Company A demands 6000 and produces 5000, a shortfall of 1000.
The comparison is against the production:
\[ \frac{6000 - 5000}{5000} \times 100 = 20\% \]
"More than" fixes the base as the smaller quantity; comparing against the demand instead would give 16.67%.
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What is the ratio of the total demand to the total production of both companies?
Answer: D
Total Demand = Demand of A + Demand of B = 6000 + 5500 = 11500 tonnes.
Total Production = Production of A + Production of B = 5000 + 6000 = 11000 tonnes.
Required Ratio = Total Demand : Total Production = 11500 : 11000.
Dividing both by 500 gives the ratio 23 : 22.
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For Company B, the production is what percent more than the demand?
Answer: C
Correct answer: 9.09%
“Percent more than the demand” takes the demand as the base, not the production.
For Company B the demand is 5500 and the production 6000, so the excess is 500.
\[\frac{6000 - 5500}{5500} \times 100 = \frac{500}{5500} \times 100 = 9.09\%\]
Dividing by the production instead would give \(\tfrac{500}{6000}\times 100 = 8.33\%\), which is how much less the demand is than the production - a different quantity, and the usual trap in this question type.
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The pie chart shows the percentage of students in a school who play five different sports. Study the chart and answer the questions that follow.
If the total number of students in the school is 1200, what is the number of students who play Cricket?
Answer: B
Cricket takes 30% of the pie.
\[ 0.30 \times 1200 = 360 \]
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The number of students who play Hockey is how many more than the number of students who play Tennis, if the total number of students is 2000?
Answer: C
Hockey is 20% and Tennis 10%, a gap of 10 percentage points.
\[ 0.10 \times 2000 = 200 \]
Working with the difference in percentages is quicker than computing 400 and 200 separately.
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If there is a 20% increase in the number of students who play football, and the total number of students remains the same (1200), what will be the new central angle for the Football sector?
Answer: B
Original number of football students = 25% of 1200 = 300.
A 20% increase means the new number is 300 * 1.20 = 360.
The new percentage of students playing football = \(\frac{360}{1200} \times 100 = 30\)%.
The new central angle = 30% of 360° = 0.30 * 360 = 108°.
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The bar graph shows the number of students enrolled (in thousands) in two different universities (A and B) in various disciplines. Study the chart and answer the questions that follow.
What is the ratio of the number of students in Arts in University A to the number of students in Commerce in University B?
Answer: D
Number of students in Arts in University A = 20,000.
Number of students in Commerce in University B = 30,000.
The required ratio is 20,000 : 30,000.
Simplifying by dividing by 10,000 gives the ratio 2 : 3.
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The number of students in Engineering in University A is what percent more than the number of students in Commerce in University A?
Answer: C
Number of students in Engineering in University A = 35,000.
Number of students in Commerce in University A = 25,000.
Increase = 35,000 - 25,000 = 10,000.
Percentage increase = \(\frac{\text{Increase}}{\text{Original Value}} \times 100 = \frac{10000}{25000} \times 100 = \frac{1}{2.5} \times 100 = 40\)%.
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What is the difference between the total number of students in University A and the total number of students in University B?
Answer: B
Add each university's four disciplines.
\[ A: 20 + 30 + 25 + 35 = 110 \text{ thousand} \]
\[ B: 25 + 35 + 30 + 30 = 120 \text{ thousand} \]
\[ 120 - 110 = 10 \text{ thousand} = 10{,}000 \]
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