Question

11. The average weight of 40 members of a society is 47.5 kg. When one of the members leaves the
society, the average weight decreases by 500 g. Find the weight of the outgoing member.
​

Answer 1

Given :

• Average Weight of 40 members = 47.5 kg
• No. of members of society = 40

To Find :

• Weight of the member who leaves the society

Solution :

We are given that the average weight of the society which have 40 members is 47.5 kg. And a men leaves the society and the average weight of society is decreased by 500 g

As we know that,

⇒Average Weight = Total Weight/ No. of persons

⇒47.5 = Total weight/40

⇒Total weight = 47.5 * 40

⇒Total weight = 1900

$\therefore$ Total weight of the society is 1900 kg

________________________________

If a member leaves the society,

• No. of members = 39
• Average weight = 47.5 - 0.5 = 47 kg

⇒Average = Total Weight/No. of members

⇒47 = Total weight/39

⇒Total weight = 47*39

⇒Total weight = 1833

$\therefore$ Now, total weight is 1833 kg

_________________________________

We've to find weight of person who leaves society

⇒Weight of member = Initial Weight - Final weight

⇒Weight of member = 1900 - 1833

⇒Weight of member = 67 kg

Answer 2

GIVEN

• The average weight of 40 members of a society is 47·5 kg.
• When one of the members leaves the  society, the average weight decreases by 500 g.

$\rule{190}3$

TO FIND

The weight of the outgoing member.

$\rule{190}3$

SOLUTION

Let the sum of the weights of all the members of the society be x.

CASE - 1

We know,

$\boxed{\sf{\ddag\ Average\ weight=\frac{Sum\ of\ all\ the\ weights}{Number\ of\ members} }}$

We get :-

$\sf{\dashrightarrow 47.5=\dfrac{x}{40} }\\\\\sf{\dashrightarrow x=47.5\times40}\\\\\sf{\dashrightarrow x=1900}$

Thus, the sum of the weights of all the members of the society is 1900 kg.

$\rule{190}{1.8}$

CASE - 2

Let the weight of the outgoing member be y.

A/q,

$\sf{\dashrightarrow 47.5\ kg-500\ g=\dfrac{x-y}{40-1} }\\\\\sf{\dashrightarrow 47.5-0.5=\dfrac{1900-y}{39} }\\\\\sf{\dashrightarrow 47\times39=1900-y}\\\\\sf{\dashrightarrow 1833=1900-y}\\\\\sf{\dashrightarrow y=1900-1833}\\\\\boxed{\sf{\dashrightarrow y=67\ kg}}$

Therefore, the weight of the outgoing member is 67 kg.