The following table shows the percentage (%) of girls who passed in an examination and the percentage (%) of boys who failed in that exam in a school during the six years from 2018 to 2023. Based on the data in the table, answer the questions that follow.
Year-wise Result details of Students
Year Percentage of Girls who passed Percentage of Boys who failed 2018 32% 40% 2019 42% 60% 2020 55% 25% 2021 40% 30% 2022 60% 50% 2023 42% 80%
Understanding Exam Results Ratio Calculation
This problem requires calculating the ratio between the number of boys who passed and the number of girls who failed in a specific year (2020), using the provided examination data.
Exam Data Table for Reference
The table below shows the percentage (%) of girls passing and the percentage (%) of boys failing over six years.
| Year | Percentage of Girls who passed | Percentage of Boys who failed |
|---|---|---|
| 2018 | 32% | 40% |
| 2019 | 42% | 60% |
| 2020 | 55% | 25% |
| 2021 | 40% | 30% |
| 2022 | 60% | 50% |
| 2023 | 42% | 80% |
Calculating the Number of Boys Passed in 2020
We are given the following information for the year 2020:
- Total number of boys appeared = 800
- Percentage of boys who failed = 25%
To find the number of boys who passed, we first need to find the percentage of boys who passed:
Percentage of boys passed = $100\% - \text{Percentage of boys who failed}$
Percentage of boys passed = $100\% - 25\% = 75\%$
Now, we calculate the total number of boys who passed:
Number of boys passed = $75\%$ of $800$
Number of boys passed = $\frac{75}{100} \times 800$
Number of boys passed = $0.75 \times 800 = 600$
Calculating the Number of Girls Failed in 2020
We are given the following information for the year 2020:
- Total number of girls appeared = 700
- Percentage of girls who passed = 55%
To find the number of girls who failed, we first calculate the percentage of girls who failed:
Percentage of girls failed = $100\% - \text{Percentage of girls who passed}$
Percentage of girls failed = $100\% - 55\% = 45\%$
Now, we calculate the total number of girls who failed:
Number of girls failed = $45\%$ of $700$
Number of girls failed = $\frac{45}{100} \times 700$
Number of girls failed = $0.45 \times 700 = 315$
Determining the Ratio
The question asks for the ratio of the total number of boys who passed to the total number of girls who failed in 2020.
Ratio = (Number of boys passed) : (Number of girls failed)
Ratio = $600 : 315$
To simplify the ratio, we find the greatest common divisor (GCD) of 600 and 315.
- Prime factorization of 600: $2^3 \times 3 \times 5^2$
- Prime factorization of 315: $3^2 \times 5 \times 7$
- GCD(600, 315) = $3 \times 5 = 15$
Now, we divide both parts of the ratio by the GCD (15):
Simplified Ratio = $\frac{600}{15} : \frac{315}{15}$
Simplified Ratio = $40 : 21$
Final Answer Explanation
The calculated ratio of the total number of boys who passed to the total number of girls who failed in 2020 is 40:21.
Important Questions from Data Interpretation
The table shows the monthly expenditure of Saumya. What percent of her monthly salary is she able to save?
Expense Amount Food 5,000 Rent 20,000 Travel 10,000 Clothing 3,000 Miscellaneous 15,000 Savings 7,500 What does the height of the rectangle in a histogram show?
Following table provides figures (in rupees) on annual expenditure of a firm for two years – 2010 and 2011.
Category
2010
2011
Raw material
5200
6240
Power & fuel
7000
9450
Salary & wages
9000
12600
Plant & machinery
20000
25000
Advertising
15000
19500
Research & Development
22000
26400
In 2011, which of the following two categories have registered increase by same percentage?
Read the following table giving sales data of five types of batteries for years 2006 to 2012
Year
Type I
Type II
Type III
Type IV
Type V
2006
75
144
114
102
108
2007
90
126
102
84
126
2008
96
114
75
105
135
2009
105
90
150
90
75
2010
90
75
135
75
90
2011
105
60
165
45
120
2012
115
85
160
100
145
Out of the following which type of battery achieved highest growth between the years 2006 and 2012?Each of the letters arranged as below represents a unique integer from 1 to 9. The letters are positioned in the figure such that (A × B × C), (B × G × E) and (D × E × F) are equal. Which integer among the following choices cannot be represented by the letters A, B, C, D, E, F and G?
A
D
B
G
E
C
F
