Question

The average age of 26 girls is 20 years.When one of them left the group the average decreased by (1)/(5) year Find the age of the girl who left.​

Answer 1

Given :

• Total number of girls = 26
• Average age = 20 years
• When one girl left , New Average age = original average age - (1/5) years

Let :

• Sum of ages of 25 girls = x years
• Age of girl , who left = y years

Formula used :

Average = Sum of observation ÷ Number of observation

Solution :

➝ Original average = Sum of age of 26 girls ÷ 26

➝ 20 = (Sum of age of 25 girls + Age of girl who left) ÷ 26

➝ 20 × 26 = x + y

➝ x + y = 520 ......... equation 1

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We know that,

New average age = Original average age - (1/5)

New average age = 20 - 0.2

New average age = 19.8

Also ,

➝ New average = (Sum of age of 25 girls )÷ 25

➝ 19.8 = x ÷ 25

➝ x = 19.8 × 25

➝ x = 495

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On putting value of x in equation 1, we get;

➝ (495) + y = 520

➝ y = 520 - 495

➝ y = 25

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ANSWER :

Age of the girl who left = 25 years