Question

Average weight of 19 men is 74 kgs, and the average weight of 38 women is 63 kgs. What is the average weight (rounded off to the nearest integer) of all the men and the women together?

• A. 59 kg
• B. 65 kg
• C. 69 kg
• D. 67 kg

Hint:

Add both total weights first, then divide by the combined headcount, not by 2.

Answer 1

The Correct Option is D

This can be solved faster with the alligation rule instead of adding up totals separately. When two groups of different sizes are combined, the combined average splits the gap between the two group averages in the inverse ratio of the group sizes.

Let the combined average be $x$. The men's average is $74$ and the women's average is $63$, with group sizes $19$ and $38$.

By alligation: $\dfrac{x - 63}{74 - x} = \dfrac{19}{38} = \dfrac{1}{2}$

Cross multiplying: $2(x - 63) = 74 - x$, so $2x - 126 = 74 - x$, which gives $3x = 200$, so $x = 66.67$.

Rounding to the nearest integer gives 67 kg, confirming option D.

\[\boxed{67 \text{ kg}}\]