Directions : The charts given below represents data of number of students of…

Concept

In a two-pie data set where one pie gives the total split (students) and the other gives a sub-group split (boys), the girls of any college equal its total students minus its boys. Each pie's slices must sum to 100%, so an unlabelled slice is found by subtracting the known slices, and the given conditions (a fixed count, or a fixed boy-girl gap) pin down the remaining unknown percentages.

Application

1. Students pie (total 2500): P = 20% = 500 and S = 25% = 625, so the two unlabelled slices satisfy Q% + R% = 100 - 20 - 25 = 55%.

2. Boys pie (total 1200): Q = 20% = 240 and R = 30% = 360, so the two unlabelled slices satisfy P% + S% = 100 - 20 - 30 = 50%.

3. Apply Note 1 (girls in Q = 10): Q students = Q boys + Q girls = 240 + 10 = 250, which is 250/2500 = 10% of students, leaving R = 55 - 10 = 45% = 1125 students.

4. Apply Note 2 (boys - girls in P = 100, boys > girls): P has 500 students, so boys + girls = 500 and boys - girls = 100, giving P boys = 300 and P girls = 200; hence P is 300/1200 = 25% of boys, leaving S = 50 - 25 = 25% = 300 boys.

5. Compute S girls = S students - S boys = 625 - 300 = 325.

6. Required quantity: boys in P and R together = 300 + 360 = 660; girls in Q and S together = 10 + 325 = 335; difference = 660 - 335 = 325.

Cross-check

Total boys = 300 + 240 + 360 + 300 = 1200 and total girls = 200 + 10 + 765 + 325 = 1300, which sum to 2500 students - both pies are internally consistent, confirming every figure used above.