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
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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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