The expenditure of a company on five heads A, B, C, D and E is in proportion to 3:5:7:11:? respectively. The expenditure on E is…

Question

The expenditure of a company on five heads A, B, C, D and E is in proportion to 3:5:7:11:? respectively. The expenditure on E is equal to the arithmetic mean of the expenditures on A and D. If the expenditure on C exceeds that on B by ₹18,000, find the total expenditure (₹) of the company.

1. A. ₹2,52,000
2. B. ₹2,97,000 (Correct answer)
3. C. ₹2,40,000
4. D. ₹1,80,000

Correct Answer

Option B — ₹2,97,000

Detailed Solution & Explanation

The correct answer is ₹2,97,000.

Key Points

• First find E's share. It is the arithmetic mean of A and D:
  • E = (3 + 11)/2 = 7
• So the full ratio is 3 : 5 : 7 : 11 : 7, totalling 33 parts.
• C exceeds B by 18,000, and C − B = 7 − 5 = 2 parts:
  • 2 parts = ₹18,000, so 1 part = ₹9,000
• Total expenditure = 33 × 9,000 = ₹2,97,000.

Additional Information

• Note that E and C both come to 7 parts, so their expenditures are equal — a useful internal check on the ratio.
• The individual amounts are A = 27,000, B = 45,000, C = 63,000, D = 99,000 and E = 63,000, which sum to ₹2,97,000 ✓.
• The general method for "the difference between two shares is given": express that difference in parts, divide to get one part, then scale.
• Ratios can be scaled freely, so always work in parts and convert to rupees only once — converting early multiplies the arithmetic.