Question

The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighting 65 kg.what is the weight of the new person​

Answer 1

Question :-

The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighting 65 kg.what is the weight of the new person.

method 1)

Solution:-

Total weight increased = (8×2.5)=20.

.°. weight of new person = (65+20)=85 kg.

method 2)

Solution:-

let the average earlier be x.

the the sum of weight of all 8 people will be 8 x.

Now,

new person replace a person and average become x+2.5(average).

.°. the total number of person are still 8, so new total of weight of all 8 people's will be 8(x+2.5) =8x+20.

so earlier the total weight of all of people was 8x. but as soon as a new person replaced a person 65(weight). the total become 8x +20 which is 20 more than the previous total,

he must be 20 more than 65 i.e 85kg.

ANSWER:- the weight of the new person is 85kg.

Answer 2

ॐ $\huge{\orange{\underline{\pink{\mathscr{Radhe}}}}}$$\huge{\orange{\underline{\green{\mathscr{Radhe}}}}}$ ॐ

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$\huge\boxed{\fcolorbox{cyan}{Yellow}{QUESTION}}$

ᴛʜᴇ ᴀᴠᴇʀᴀɢᴇ ᴡᴇɪɢʜᴛ ᴏғ 8 ᴘᴇʀsᴏɴ's ɪɴᴄʀᴇᴀsᴇs ʙʏ 2.5 ᴋɢ ᴡʜᴇɴ ᴀ ɴᴇᴡ ᴘᴇʀsᴏɴ ᴄᴏᴍᴇs ɪɴ ᴘʟᴀᴄᴇ ᴏғ ᴏɴᴇ ᴏғ ᴛʜᴇᴍ ᴡᴇɪɢʜᴛɪɴɢ 65 ᴋɢ.ᴡʜᴀᴛ ɪs ᴛʜᴇ ᴡᴇɪɢʜᴛ ᴏғ ᴛʜᴇ ɴᴇᴡ ᴘᴇʀsᴏɴ

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$\huge\boxed{\fcolorbox{cyan}{Yellow}{SOLUTION }}$

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➀ $\huge{\orange{\underline{\red{\mathbf{Method\:}}}}}$

ʟᴇᴛ ᴡᴇ sᴀʏ ᴛʜᴀᴛ ᴀᴠᴇʀᴀɢᴇ ᴇᴀʀʟɪᴇʀ ʙᴇ $x$

$\implies$ sᴜᴍ ᴏғ ᴡᴇɪɢʜᴛ ᴏғ ᴀʟʟ 8 ᴘᴇᴏᴘʟᴇ ᴡɪʟʟ ʙᴇ $8x$

$\implies$ ɴᴇᴡ ᴘᴇʀsᴏɴ ʀᴇᴘʟᴀᴄᴇ ᴀ ᴘᴇʀsᴏɴ & ᴀᴠᴇʀᴀɢᴇ ʙᴇᴄᴏᴍᴇ $x+2.5$(ᴀᴠɢ).

$\implies$$\therefore$ ᴛʜᴇ ᴛᴏᴛᴀʟ ɴᴜᴍʙᴇʀ ᴏғ ᴘᴇʀsᴏɴ ᴀʀᴇ sᴛɪʟʟ $8$

$\implies$ sᴏ, ɴᴇᴡ ᴛᴏᴛᴀʟ ᴏғ ᴡᴇɪɢʜᴛ ᴏғ ᴀʟʟ 8 ᴘᴇᴏᴘʟᴇs ᴡɪʟʟ ʙᴇ $8(x+2.5)=8x+20$

$\implies$ sᴏ, ᴇᴀʀʟɪᴇʀ ᴛʜᴇ ᴛᴏᴛᴀʟ ᴡᴇɪɢʜᴛ ᴏғ ᴀʟʟ ᴏғ ᴘᴇᴏᴘʟᴇ ᴡᴀs $8x$. ʙᴜᴛ sᴏᴏɴ ᴀs ᴀ ɴᴇᴡ ᴘᴇʀsᴏɴ ʀᴇᴘʟᴀᴄᴇᴅ ᴀ ᴘᴇʀsᴏɴ $65(weight)$. ᴛʜᴇ ᴛᴏᴛᴀʟ ʙᴇᴄᴏᴍᴇ $8x+20$ ᴡʜɪᴄʜ ɪs $20$ ᴍᴏʀᴇ ᴛʜᴀɴ ᴛʜᴇ ᴘʀᴇᴠɪᴏᴜs ᴛᴏᴛᴀʟ.

$\implies$ $\therefore$ ᴛʜᴇ ᴘᴇʀsᴏɴ ᴍᴜsᴛ ʙᴇ $20$ ᴍᴏʀᴇ ᴛʜᴀɴ $65$ ɪ.ᴇ., $85kg$.

$\pink{The\:weight\:of\:new\: person\:=}$$\red{85kg}$

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➁ $\huge{\orange{\underline{\red{\mathbf{Method\:}}}}}$

$\implies$ Total increased weight = $(8×2.5)=20$

$\implies$ $\therefore$ Weight of new person = $(65+20)$= $\red{85kg}$

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