Read the following table carefully and answer the question that follows. The…
2020
Read the following table carefully and answer the question that follows.
The following table embodies the details about the students of the different departments A, B and C in a University for participating in the blood donation camp.
Participation in Blood Donation Camp - Data
* Out of total blood donors.
Ques: What is the ratio of the number of blood donors in the department 'A' compared to the number of blood donors in 'B'?
- A.
1:5
- B.
2:5
- C.
9:16
- D.
8:15
Show answer & explanation
Correct answer: D
Concept
When a table gives one sub-group's share as a percentage "out of total donors" and gives the other sub-group's actual count, the two percentages must add to 100% of that total. So the whole can be recovered as: (given count) ÷ (that sub-group's percentage of the total, written as a decimal).
Step-by-step solution
In department A, girls make up 40% of the blood donors (marked *), so boys make up 100% − 40% = 60% of A's donors.
The 48 boy donors in A therefore represent 60% of A's total donors, so total donors in A = 48 ÷ 0.60 = 80.
In department B, girls make up 50% of the blood donors, so boys also make up 100% − 50% = 50% of B's donors.
The 75 boy donors in B therefore represent 50% of B's total donors, so total donors in B = 75 ÷ 0.50 = 150.
Ratio of total donors in A to total donors in B = 80 : 150. Dividing both terms by 10 gives 8 : 15.
Cross-check
Check: in A, girls donors = 40% of 80 = 32, and 32 + 48 = 80, which matches A's total; in B, girls donors = 50% of 150 = 75, and 75 + 75 = 150, which matches B's total. This confirms 8 : 15.