Directions : Read the following pie chart and table carefully and answer the…
2024
Directions : Read the following pie chart and table carefully and answer the questions given below. The pie chart shows the percentage and degree distribution of the total number of students in four different institutions that provide skill development courses. The table shows the given institutions provide training for students to another institution.
If the difference between the C provides training to students and total number of students in D is Z, then find which of the following option is correct about Z.
- A.
X²
- B.
Y²
- C.
(Y-X)²
- D.
Y/X
- E.
Both X2 and (Y - X)2
Show answer & explanation
Correct answer: E
Concept
In a pie chart, a sector's central angle and its percentage are proportional to the same whole: percentage = (angle / 360) x 100, and a sector's count = (angle / 360) x Total. Two relations are first used to pin every unknown: (i) all four percentages add up to 100, and (ii) one externally given count fixes the remaining variable. "Provides training to" means an institution trains the students belonging to the institution(s) named in the table, so its training count equals the sum of those institutions' student counts.
Application
Convert the known angles. B = 108 degrees gives B% = 108/360 x 100 = 30%, so B = 30% of 2000 = 600. D = 54 degrees gives D% = 54/360 x 100 = 15%, so D = 15% of 2000 = 300.
Use the note: B trains "Both C and D", so B's training count = C + D = 1000. With D = 300, C = 1000 - 300 = 700, i.e. C% = 700/2000 x 100 = 35%. Since C% = (X+25)%, we get X = 35 - 25 = 10.
Use the 100% closure: Y + 30 + (X+25) + 15 = 100, so X + Y = 30, giving Y = 30 - 10 = 20. Hence A = Y% = 20% of 2000 = 400. (Check: A+B+C+D = 400+600+700+300 = 2000.)
C provides training to "Only A", so C's training count = A = 400. Total students in D = 300. Therefore Z = |400 - 300| = 100.
Cross-check
Compare Z = 100 against each expression with X = 10, Y = 20: X2 = 100, Y2 = 400, (Y - X)2 = (20 - 10)2 = 100, and Y/X = 2. Z equals both X2 and (Y - X)2, so the value matching Z is given by both of those expressions together.