A group of 74 Class XI students went on a picnic. The number of students from…

2020

A group of 74 Class XI students went on a picnic. The number of students from each section was:

Section

Number of students

A

15

B

24

C

15

D

20

Five students from Section A spent as much as four students from Section B. Twelve students from Section B spent as much as nine students from Section C, and six students from Section C spent as much as eight students from Section D. Every student within a section spent the same amount. If all 74 students spent Rs 23,370 altogether, find the amount spent by each student from Section D.

Answer: A. Rs 307.50 — Concept: In a chained-ratio problem, pairwise equalities connect several unknown quantities. Choose one unknown as a reference, express every other unknown as…

  1. A.

    Rs 307.50

  2. B.

    Rs 410

  3. C.

    Rs 246.50

  4. D.

    Rs 369

Attempted by 32 students.

Show answer & explanation

Correct answer: A

Concept: In a chained-ratio problem, pairwise equalities connect several unknown quantities. Choose one unknown as a reference, express every other unknown as its multiple, and substitute those expressions into the total-value equation.

Application: Let a, b, c and d be the amounts spent by each student in Sections A, B, C and D, respectively. We use d as the reference because the question asks for the Section D amount.

  1. From five Section A students spending as much as four Section B students, 5a = 4b, so a = (4/5)b.

  2. From twelve Section B students spending as much as nine Section C students, 12b = 9c. Dividing by 12 gives b = (3/4)c.

  3. From six Section C students spending as much as eight Section D students, 6c = 8d. Dividing by 6 gives c = (4/3)d.

  4. Substitute c = (4/3)d into b = (3/4)c: b = (3/4) × (4/3)d = d.

  5. Substitute b = d into a = (4/5)b: a = (4/5)d.

  6. Use the numbers of students in the four sections: 15a + 24b + 15c + 20d = 23,370.

  7. Replace a, b and c by their expressions in d: 15 × (4/5)d + 24d + 15 × (4/3)d + 20d = 23,370.

  8. Simplify each term: 12d + 24d + 20d + 20d = 23,370, so 76d = 23,370.

  9. Divide by 76: d = 23,370 ÷ 76 = Rs 307.50.

Cross-check: a = Rs 246, b = Rs 307.50, c = Rs 410 and d = Rs 307.50. The four section totals are Rs 3,690, Rs 7,380, Rs 6,150 and Rs 6,150; their sum is Rs 23,370.

Therefore, each student from Section D spent Rs 307.50.

Explore the full course: Iocl Engineers Officer Grade A Paper 1

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