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).
Total number of boys in college S is what percent of number of total students in college P.
- A.
60%
- B.
40%
- C.
50%
- D.
80%
- E.
20%
Show answer & explanation
Correct answer: A
Concept
In a pie-chart data set, each sector's percentage is taken of that chart's stated grand total, so an absolute count = (sector % × grand total)÷100. When a sector's share is hidden, recover it from the constraint that all sectors of one chart sum to 100%. To express one quantity as a percentage of another, use: required % = (part ÷ whole) × 100, taking each absolute count from the correct chart (students from the 2500-chart, boys from the 1200-chart).
Applying it to this data
Students in college P = 20% of 2500 = 500. This is the "whole" the question asks the percentage of.
Find boys in college S. The boys-chart total is 1200, with Q = 20% and R = 30% shown. P's boys share is still unknown, so first fix it using the boys–girls gap in P.
In college P: total students = 500, and boys − girls = 100 with boys greater. Solving boys + girls = 500 and boys − girls = 100 gives boys = 300, girls = 200. So P's boys = 300, which is 300÷1200 = 25% of all boys.
Boys in P and S together make up the remaining share of the boys-chart: 100% − 20% (Q) − 30% (R) = 50%. Since P takes 25%, S's boys share = 50% − 25% = 25%.
Boys in college S = 25% of 1200 = 300.
Required percentage = (boys in S ÷ students in P) × 100 = (300 ÷ 500) × 100 = 60%.
Cross-check
Verify the hidden student-shares are consistent: girls in Q = 10 and boys in Q = 20% of 1200 = 240, so Q has 250 students = 10% of 2500. Then R = 100% − 20% − 10% − 25% = 45%, a valid positive share — the figures are internally consistent. The ratio 300:500 reduces to 3:5 = 60%, confirming the result.