The monthly salary of a person was ₹1,60,000. He used to spend on three heads – Personal and family expenses (P), Taxes (T), and Education loan (E). The rest were his savings. P wa... The monthly salary of a person was ₹1,60,000. He used to spend on three heads – Personal and family expenses (P), Taxes (T), and Education loan (E). The rest were his savings. P was 50% of the income, E was 20% of P, and T was 15% of E. When his salary got raised by 30%, he maintained the percentage level of P, but E became 30% of P and T became 20% of E. The sum of the two savings (in ₹) is: Which institute has the second highest percentage of students who passed to the students who appeared from that institute?
Understand the Problem
The question presents mathematical problems involving salaries, percentages, pie charts, and filling pipes. It requires calculations to determine values based on the given scenarios.
Answer
D
Answer for screen readers
The institute with the second highest percentage of students who passed is D.
Steps to Solve
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Identify the total number of students The total number of students that appeared in the examination is given as 1200.
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Calculate the percentage of students passed from each institute Using the pie chart for each institute:
- For A: $54^\circ$ corresponds to $\frac{54}{360} \times 1200$
- For B: $90^\circ$ corresponds to $\frac{90}{360} \times 1200$
- For C: $39^\circ$ corresponds to $\frac{39}{360} \times 1200$
- For D: $105^\circ$ corresponds to $\frac{105}{360} \times 1200$
- For E: $72^\circ$ corresponds to $\frac{72}{360} \times 1200$
- Calculate number of students passed from each institute
- For A: $$ \text{Students from A} = \frac{54}{360} \times 1200 = 180 $$
- For B: $$ \text{Students from B} = \frac{90}{360} \times 1200 = 300 $$
- For C: $$ \text{Students from C} = \frac{39}{360} \times 1200 \approx 130 $$
- For D: $$ \text{Students from D} = \frac{105}{360} \times 1200 \approx 350 $$
- For E: $$ \text{Students from E} = \frac{72}{360} \times 1200 = 240 $$
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Find the total number passed from each institute Now we gather these numbers to see which institute has the second highest percentage.
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Calculate the percentages of passed students For the second pie chart:
- From A to E passed students (in percentage):
- A: 18%
- B: 15%
- C: 30%
- D: 28%
- E: 9%
- Determine the second highest percentage List the percentages:
- C: 30%
- D: 28%
- A: 18%
- B: 15%
- E: 9%
From this, the second highest percentage is from D (28%).
The institute with the second highest percentage of students who passed is D.
More Information
The calculations show the importance of understanding how to interpret pie charts to derive useful numerical data. Using angles to determine proportions is a common and useful mathematical approach.
Tips
- Misinterpreting degrees in the pie chart could lead to incorrect calculations.
- Forgetting to convert from degrees to an actual number of students.
