Question

The average weight of 12 people gets increased by 3.5kg when a person weighs 56 kg got replaced by another man. Find the weight of the new man

Answer 1

$<b>$
Let Average weight of 12 people be x
Average = $\frac{Sum}{Number}$

$\frac{Sum\: of\: weights\: of\: people}{12} = x$

$\implies$ Sum of weights of people = 12x

Now,
When a person got replaced by another, Average gets increased by 3.5 kg

$\frac{Sum\: of\: weights\: of\: people}{12} = x+3.5$

$\implies$ Sum of weights of people = 12(x+3.5)

The difference between both the sums is the weight of new heavier person that was added.

Weight of heavier person = 12(x+3.5)-12x

$\implies$42 kg

Therefore,
weight of Heavier person = 42kg

So the new guy weights 42 kg more than the old guy.
So new guy weights: 56 + 42 = 98kg

Answer 2

The weight of the new man = 98 kg

Given :

The average weight of 12 people gets increased by 3.5kg when a person weighs 56 kg got replaced by another man

To find :

The weight of the new man

Solution :

Step 1 of 2 :

Form the equation to find the weight of the new man

Let average weight of 12 people before the person is replaced is w kg

∴ The total weight of 12 people before the person is replaced is 12w kg

Let the weight of the new man = x kg

A person weighs 56 kg got replaced by another man of x kg

∴ The total weight of 12 people after replacement

= (12w + x - 56) kg

Now the new average of 12 people after replacement = (w + 3.5) kg

By the given condition

$\displaystyle \sf \frac{12w + x - 56}{12} = w + 3.5$

Step 2 of 2 :

Find weight of the new man

$\displaystyle \sf \frac{12w + x - 56}{12} = w + 3.5$

$\displaystyle \sf{ \implies }12w + x - 56 = 12(w + 3.5)$

$\displaystyle \sf{ \implies }12w + x - 56 = 12w + 42$

$\displaystyle \sf{ \implies } x - 56 = 42$

$\displaystyle \sf{ \implies } x = 56 + 42$

$\displaystyle \sf{ \implies } x =98$

Hence the weight of the new man = 98 kg

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