Question : An army of 12000 consists of Europeans and Indians. The average height of a European is 5 ft 10 inches and that of an Indian is 5 ft 9 inches and that of the whole army is 5 ft $9\frac{3}{4}$ inches. Then the number of Indians in the army is:
Option 1: 3000
Option 2: 4000
Option 3: 5500
Option 4: 2700
Correct Answer: 3000
Solution :
Given: Average height of a European = 5 feet 10 inches
Average height of an Indian = 5 feet 9 inches
Average height of the army = 5 feet $9\frac{3}{4}$ inches
By using alligation method, we get:
European = 5 feet $9\frac{3}{4}$ inches – 5 feet 9 inches = $\frac{3}{4}$
Indian = 5 feet 10 inches – 5 feet $9\frac{3}{4}$ inches = $\frac{1}{4}$
$\therefore$ The ratio of European : Indian = 3 : 1
Thus, number of Indians in the army = $\frac{1}{4}×12000 = 3000$
Hence, the correct answer is 3000.
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