Multiple choice

Passage

Directions: Read the following passage and answer the question. A university has 1500 students in the final year of engineering with the number of girls 12.5% less than the number of boys. The students in the final year are in different branches viz. ECE, EE, CSE, IT and ME. The number of girls in EE branch in the final year and the number of girls in ME branch in the final year are in the ratio of 4 : 5. The ratio of boys to girls in the final year of ME branch is 2 : 1. The number of girls in ECE branch in the final year is 20% more than the number of girls in ME branch in the final year. 75 girls are in IT branch in the final year. The number of boys in CSE branch is 80. The number of boys in IT branch in the final year and the number of girls in ECE branch in the final year are in the ratio of 2 : 7. The number of boys in EE branch in the final year is 50% more than the number of girls in EE branch in the final year. The number of boys in ECE branch in the final year is equal to the number of girls in CSE branch in the final year.

If the data on the number of students in each branch in the final year is represented in the form of a pie chart, what will be the measure of the central angle corresponding to the number of students in ECE branch in the final year?

  1. 59.8°

  2. 65.4°

  3. 74.4°

  4. 81.2°

  5. 85.4°
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Based on the given ratios and counts, the total number of students is 1500. Calculating the number of students in the ECE branch requires solving the system of linear equations provided for each branch. The calculated number of students in ECE is 310, and the central angle is (310/1500) * 360 degrees, which equals 74.4 degrees.

AI explanation

Let the number of boys be x, so the number of girls is 0.875x, and the total is 1.875x = 1500, giving 800 boys and 700 girls. Using the given ratios, the number of girls in ECE is 250 and the number of boys in ECE is 60, so the total number of students in ECE is 310. The pie chart angle for ECE is 310 / 1500 * 360 degrees, which equals 74.4 degrees.

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