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 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 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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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 |
For Company B, the production is what percent more than the demand?
Answer: C
For Company B: Production = 6000, Demand = 5500. Let me check the table. No, the table in the earlier question was different. Using the table from Question 100: Demand=600, Production=1800.
Excess production = 1800 - 600 = 1200.
Percentage more = \(\frac{\text{Excess}}{\text{Demand}} \times 100 = \frac{1200}{600} \times 100 = 2 \times 100 = 200\)%.
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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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The demand for product of company B is what percent of the demand for product of company A?
Answer: B
Demand for company B = 600 tonnes.
Demand for company A = 3000 tonnes.
Required percentage = \(\frac{600}{3000} \times 100 = \frac{1}{5} \times 100 = 20\)%.
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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 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 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
Percentage for Hockey = 20%.
Percentage for Tennis = 10%.
The difference in percentage is 20% - 10% = 10%.
The difference in the number of students = 10% of 2000
= 0.10 × 2000 = 200.
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If the total number of students in the school is 1200, what is the number of students who play Cricket?
Answer: B
The percentage of students who play Cricket is 30%.
Number of students who play Cricket = 30% of 1200
= 0.30 × 1200 = 360.
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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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What is the difference between the total number of students in University A and the total number of students in University B?
Answer: B
Total students in University A = 20 + 30 + 25 + 35 = 110 thousand.
Total students in University B = 25 + 35 + 30 + 30 = 120 thousand.
Difference = 120,000 - 110,000 = 10,000.
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