1.

After replacing an old member by a new member, it was found that the average age of five members of a club is the same as it was 3 years ago. The difference between the ages of the replaced and the new members is1). 2 years2). 4 years3). 8 years4). 15 years

Answer»

Average = (sum of observation/no of observation)

Let, Present age of the OLD MEMBER who is replaced = x years

Present age of the new member = y years

Present average of 5 members = z years

Sum of present age of other 4 old member = m years

Given, Number of member = 5

Present average ages of 5 members including the new member

= (Sum of age of the four old member + y)/5 = (m + y)/5

Again, 3 years ago,

Sum of the ages of 5 members including the old member3 years ago,

= {Sum of present age of the other four old member – (4 × 3)}+ (x – 3)

= (m – 12) + (x – 3)

∴ Average of 5 members 3 years ago

= {(m – 12)+ (x – 3)}/5

According to the question

Present average = Average 3 years ago

⇒ (m + y)/5= {(m – 12)+ (x – 3)}/5

⇒ m + y = (m – 12) + (x – 3)

⇒ y = x – 15

⇒ x – y = 15 years


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