Discussion

Question:

The total population of a town consists of 6,000 men and women. The average height of a man is 165 cm and that of a woman is 155 cm. and that of the whole population is 162.5 cm. Find the number of women in the town.

Explanation:

Let m be the number of men

Then, (6000 – m) = number of women

By the problem, $\frac{m \times 165 + (6000 - m) \times 155}{6000}$ = 162.5

⇒ 165m + 930000 – 155m = 975000

⇒ 10m = 45,000 or m = 4500

∴ Number of women = 6,000 – 4,500 = 1,500.

Hence, option (a).

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