Directions : The charts given below represents data of number of students of…
2021
Directions : The charts given below represents data of number of students of four colleges P, Q, R and S. Based on the information given below, answer the questions that follow:
Note: 1. Number of girls in college Q is 10.
2. Difference between number of boys and girls in college P is 100. (Number of boys is greater than number of girls).
If 10% of boys from school S scored more than 90% in an exam, then find maximum number of boys who scored less than 90%.
- A.
240
- B.
200
- C.
270
- D.
250
- E.
220
Show answer & explanation
Correct answer: C
Concept
In a pie-chart data-interpretation set, a sector's value = (sector percentage) x (the chart total). When two charts share categories (here students and boys), the number of girls in any college = its students minus its boys. Two stated conditions then pin down the unknown sectors, after which every count is fixed.
Setting up the totals
Total students = 2500; sectors P = 20%, S = 25%, with Q and R unknown (their two shares add to 55%).
Total boys = 1200; sectors Q = 20%, R = 30%, with P and S unknown (their two shares add to 50%).
Total girls = 2500 - 1200 = 1300.
Applying the two conditions
Boys in Q = 20% of 1200 = 240. Girls in Q are given as 10, so students in Q = 240 + 10 = 250, i.e. Q = 250/2500 = 10% of students; hence R = 55% - 10% = 45%.
Students in P = 20% of 2500 = 500. With boys - girls = 100 and boys + girls = 500, solving gives P boys = 300 and P girls = 200.
P boys = 300 = 300/1200 = 25% of boys, so the remaining S share of boys = 50% - 25% = 25%. Therefore boys in S = 25% of 1200 = 300.
Answering the question
Boys in school S = 300. Exactly 10% of them scored more than 90%, i.e. 10% of 300 = 30 boys. The remaining 90% scored 90% or below, so the maximum number of boys who scored less than 90% = 90% of 300 = 270.
Cross-check
Boys account across colleges: P 300 + Q 240 + R 360 + S 300 = 1200, matching the given total of boys. The 30 high-scorers plus 270 others rebuild the 300 boys in S, confirming the count.