Question

# A lift can carry up to $8$ persons. At the ground floor$A,B,C$ whose weights are in increasing AP with an average weight of $62kg$ enter the lift. When the lift stops at $3rd$ floor $E,FandG$ whose weights are in an increasing AP enter the lift. The new average weight of people in the lift becomes $66kg$. What is the weight of F?

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Solution

## Step 1: Find the total weight of $A,B,C$The weights of $A,B,C$ are in increasing APLet$a-d,a,a+d$ be the weights of $A,B,C$the total weight of $A,B,C=a-d+a+a+d=3a$Now, the average weight of $A,B,C=\frac{Totalweight}{3}=\frac{3a}{3}=a$According to the problem $a=62kg.$Total Weight of $A,B,C$ $=3x62=186kg$Step 2: Find the total weight of all six persons.The weights of $E,FandG$ are in increasing APLet$b-d,b,b+d$ be the weights of $E,FandG$Total weight of $E,FandG=b-d+b+b+d=3b$Total weight of six persons$=186+3b$According to the problem the average weight of people in the lift is $66kg$Total Weight of six persons$=66x6=396kg$Step 3: Find the weight of $F.$$⇒186+3b=396\phantom{\rule{0ex}{0ex}}⇒3b=210\phantom{\rule{0ex}{0ex}}⇒b=70$Hence, the weight of$F=70kg$

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