A group of 74 students of Class XI went on picnic. The number of students who…
2020
A group of 74 students of Class XI went on picnic. The number of students who went on picnic by each section is as follows:
Section A = 15
Section B = 24
Section C = 15
Section D = 20
5 students from Section A spent as much as 4 students from Section B.
12 students from Section B spent as much as 9 students from Section C and 6 students from Section C spent as much as 8 students from Section D.
If every student of a particular section spent the same amount and all the students spent Rs 23,370 altogether, find the amount spent by each student of Section D.
- A.
Rs 307.50
- B.
Rs 410
- C.
Rs 369
- D.
Rs 246.50
Attempted by 22 students.
Show answer & explanation
Correct answer: A
- Let the expenditure of a single student in sections A, B, C, and D be a, b, c, and d respectively.
- Step 1: Establish the relational equations from the problem statement: 5a = 4b -> a = (4/5)b 12b = 9c -> c = (12/9)b = (4/3)b 6c = 8d -> d = (6/8)c = (3/4)c
- Step 2: Convert all variables into terms of 'b' to create a unified ratio: a = 0.8b c = 1.333b d = (3/4) (4/3)b = b
- Step 3: Set up the total expenditure equation using the student counts (A=15, B=24, C=15, D=20):
Total Expense = 15a + 24b + 15c + 20d = 23,370
Substitute the values: 15(4/5)b + 24b + 15(4/3)b + 20(b) = 23,370
Simplify: 12b + 24b + 20b + 20b = 23,370 76b = 23,370 b = 23,370 ÷ 76 = 307.50
- Step 4: Find the expenditure for Section D: * Since d = b, a student of Section D spent exactly Rs 307.50.