Study the charts given below carefully and answer the following questions. Pie…
2021
Study the charts given below carefully and answer the following questions. Pie chart shows the percentage distribution of total students (Science +Commerce) in 12th class of five different Zones and table shows the number of students in same class in science of same zones.
If Western zone also have Arts students and ratio of sum of students of science and commerce in western zone and Arts students in western zone is 5 : 7, then find Arts students in western zone are how much more than commerce students in Southern zone.
- A.
1510
- B.
1430
- C.
1570
- D.
1620
- E.
1690
Show answer & explanation
Correct answer: A
Concept
In a pie chart each zone's slice is a percentage of one fixed total, so a zone's count = (its percent) × (total). When a category is split into parts (here Science + Commerce), an unknown part is found by subtraction: Commerce = (Science + Commerce) − Science. A part given only as a ratio is found by scaling: if A : B = 5 : 7, then B = A × 7/5.
Application
Total (Science + Commerce) = 4000. Western zone is 30% of this, so Western (Science + Commerce) = 30% × 4000 = 1200.
Western Arts is given by the ratio (Western Science + Commerce) : (Western Arts) = 5 : 7, so Western Arts = 1200 × 7/5 = 1680.
Southern zone is 15% of the total, so Southern (Science + Commerce) = 15% × 4000 = 600. From the table Southern Science = 430, so Southern Commerce = 600 − 430 = 170.
Required difference = Western Arts − Southern Commerce = 1680 − 170 = 1510.
Cross-check
Re-scale to confirm: 1200/5 = 240 is one ratio unit, and Western Arts = 7 units = 7 × 240 = 1680, which agrees. Subtracting Southern Commerce 170 gives 1680 − 170 = 1510.