Question
Download Solution PDFIn a police battalion of 600 police, the average height is 150 cm. Later it is discovered that for x policemen heights are copied wrongly as 160 cm instead of 190 cm. By taking the correct heights, the average is increased to 155 cm. Then x =
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Number of police = 600
Initial average height = 150 cm
Corrected average height = 155 cm
Height wrongly recorded for x policemen = 160 cm
Actual height of x policemen = 190 cm
Formula used:
New total height = Corrected average × Total number of police
Wrong total height = Initial average × Total number of police
Difference = Change caused by x policemen
Change caused by x policemen = x × (Actual height - Wrongly recorded height)
Calculation:
New total height = 155 × 600 = 93000
Wrong total height = 150 × 600 = 90000
⇒ Difference = New total height - Wrong total height
⇒ Difference = 93000 - 90000 = 3000
⇒ Change caused by x policemen = x × (190 - 160)
⇒ 3000 = x × 30
⇒ x = 100
∴ The correct answer is option (2).
Last updated on Sep 27, 2023
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