A ₹36,000 annual bonus is distributed among Sales, Marketing, and Operations in a 4:5:3 ratio. Marketing uses ₹3,000 for team building and ₹1,500 for an intern, then allocates the rest to two top performers in a 5:4 ratio. How much does the top performer with the smaller share receive?

Correct — C. Find Marketing's share, take out the two expenses, then split what is left.

Total ratio parts: 4 + 5 + 3 = 12
Marketing's share: 5⁄12 × 36,000 = ₹15,000

Subtract the expenses: 15,000 − 3,000 − 1,500 = ₹10,500
Parts for the two performers: 5 + 4 = 9

Smaller share: 4⁄9 × 10,500 = 42,000⁄9 = ₹4,666.67 → option (c)

Why the others are wrong

• (a)
  ₹5,833.33 — ₹5,833.33 is the larger share, 5⁄9 × 10,500. The question asks for the performer with the smaller share, who gets the 4 parts.
• (b)
  ₹5,250 — ₹5,250 is half of ₹10,500, an equal split. The 5 : 4 ratio gives unequal shares of ₹5,833.33 and ₹4,666.67.
• (d)
  ₹4,200 — ₹4,200 is 4⁄10 of ₹10,500, as if the ratio had 10 parts. But 5 + 4 = 9, so each part is 10,500 ÷ 9 ≈ ₹1,166.67.

Share = (its ratio parts ÷ total parts) × amount. When the total is known, start by adding the parts.

Here the split happens in two stages, with a subtraction between them. Marketing's 5 of 12 parts is ₹15,000, and just the ₹10,500 left after ₹4,500 of expenses is divided 5 : 4.

Key facts

• In a ratio a : b : c, one part = total ÷ (a + b + c).
• 36,000 ÷ 12 = ₹3,000 per part, so Marketing's 5 parts are ₹15,000.
• The two shares of a split add back to the amount split: ₹5,833.33 + ₹4,666.67 = ₹10,500.

Common traps

• Splitting ₹15,000 in 5 : 4 before subtracting the ₹4,500 of expenses.
• Picking the 5-part share. The smaller share is the 4 parts, 4⁄9 of the remainder.

No directly related past PYQ was found.