The following line graph shows the population of a town (in thousands) in different years. Study the graph and answer the questions that follow.
The population in 2016 was what percentage of the population in 2020?
Answer: B
Read the two years off the graph: 55 thousand in 2016 and 82 thousand in 2020.
\[ \frac{55}{82} \times 100 = 67.07\% \]
The base is the 2020 figure, since the question asks what 2016 was of 2020.
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The table below shows the percentage distribution of 1400 students who passed in an exam from five different cities.
| City | % of Passed Students |
|---|---|
| A | 12% |
| B | 18% |
| C | 25% |
| D | 20% |
| E | 25% |
What is the number of students who passed from city C?
Answer: C
City C accounts for 25% of the 1400 who passed.
\[ 0.25 \times 1400 = 350 \]
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The number of students passed from city B is what percentage of the number of students passed from city D?
Answer: C
Since the total number of students is the same for all calculations, we can work directly with the percentages.
Percentage from city B = 18%.
Percentage from city D = 20%.
Required percentage = \(\frac{18}{20} \times 100 = 90\)%.
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What is the difference between the number of students passed from cities C and E combined, and the number of students passed from cities A and B combined?
Answer: B
Percentage for C and E = 25% + 25% = 50%.
Percentage for A and B = 12% + 18% = 30%.
The difference in percentage = 50% - 30% = 20%.
The difference in number of students = 20% of 1400 = 0.20 * 1400 = 280.
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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 Company Y in 2018 was Rs. 600 crores, what was its expenditure in that year?
Answer: B
Profit % = \(\frac{\text{Income} - \text{Expenditure}}{\text{Expenditure}} \times 100\).
Let E be the expenditure.
In 2018, the profit percentage for Company Y was 40%.
40 = \(\frac{600 - E}{E} \times 100\)
0.40 = \(\frac{600}{E} - 1\)
1.40 = \(\frac{600}{E}\)
E = \(\frac{600}{1.4} = \frac{6000}{14} \approx 428.57\) crores.
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If the expenditure of Company X in 2017 and Company Y in 2017 were equal, what was the ratio of their incomes in 2017?
Answer: A
Let the equal expenditure for both companies in 2017 be E.
Income = Expenditure × (1 + \(\frac{\text{Profit %}}{100}\)).
For Company X in 2017, Profit = 45%. Income_X = E × (1 + 0.45) = 1.45E.
For Company Y in 2017, Profit = 50%. Income_Y = E × (1 + 0.50) = 1.50E.
Ratio of Incomes (X:Y) = 1.45E : 1.50E = 1.45 : 1.50 = 145 : 150.
Dividing by 5 gives the ratio 29 : 30.
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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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