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Question

A lift can carry up to 8 persons. At the ground floorA,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 AP

Leta-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=Totalweight3=3a3=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 AP

Letb-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=3963b=210b=70

Hence, the weight ofF=70kg


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