A company has 80 employees, of whom 35 % are women. The average monthly salary of the women is ₹72,000, while that of the men is ₹68,000. What is the overall average monthly salary (in ₹ 000) of the whole workforce?

Correct — D.
Women = 35% of 80 = 28
Men = 80 − 28 = 52

Women's total = 28 × 72 = 2016 (₹ 000)
Men's total = 52 × 68 = 3536 (₹ 000)
Whole payroll = 2016 + 3536 = 5552 (₹ 000)

Average = 5552 ÷ 80 = 69.4 (₹ 000), that is ₹69,400 → option (d).

Why the others are wrong

• (a)
  70.8 — 70.8 is above the midpoint of 70, and that would need more women than men. Men are 52 of the 80 and earn less, so the overall mean must fall below 70.
• (b)
  699.4 — 699.4 lies outside the 68–72 range. An overall average always sits between the group averages, so no split of these 80 salaries can reach 699.4 thousand.
• (c)
  245.4 — 245.4 is more than three times the higher group average. The overall mean of two groups must lie between their averages, 68 and 72, so 245.4 is impossible.

A weighted average combines group averages in proportion to group size: (n₁a₁ + n₂a₂) ÷ (n₁ + n₂).

Here the weights are 28 women and 52 men. The men outnumber the women, so the answer sits closer to 68 than to 72.

A faster route uses the gap: 68 + 4 × 0.35 = 68 + 1.4 = 69.4, where 4 is the salary gap and 0.35 is the women's share.

Key facts

• Weighted average = (n₁a₁ + n₂a₂) ÷ (n₁ + n₂).
• An overall average always lies between the lowest and highest group averages.
• The overall average sits nearer the average of the larger group.
• Shortcut: lower average + gap × share of the higher-paid group = 68 + 4 × 0.35 = 69.4.

Common traps

• Taking the simple mean of 72 and 68, which gives 70 and ignores the 28 : 52 split.
• Attaching the 35% to the men's salary instead of the women's, which gives 70.6.

No directly related past PYQ was found.