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 Section B students spent as much as 9 Section C students and 6 Section C students spent as much as 8 Section D student. 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 246.50
- D.
Rs 369
Attempted by 6 students.
Show answer & explanation
Correct answer: A
Let the amount spent per student in Sections A, B, C, D be a, b, c, d respectively.
Translate the given conditions into ratios:
5a = 4b ⇒ a = (4/5)b
12b = 9c ⇒ b = (3/4)c
6c = 8d ⇒ c = (4/3)d
Express everything in terms of d (the per-student amount for Section D):
c = (4/3)d, b = (3/4)c = (3/4)×(4/3)d = d, a = (4/5)b = (4/5)d
Now form the total-spending equation using the number of students in each section (A = 15, B = 24, C = 15, D = 20):
15a + 24b + 15c + 20d = 23,370
15×(4/5)d + 24×d + 15×(4/3)d + 20×d = 23,370
12d + 24d + 20d + 20d = 23,370
76d = 23,370 ⇒ d = 23,370 ÷ 76 = 307.50
Therefore, each student of Section D spent Rs 307.50.
Check: a = 246, b = 307.50, c = 410, d = 307.50, giving section totals 3,690 + 7,380 + 6,150 + 6,150 = 23,370. ✓
Hence the correct answer is Rs 307.50.