Question

the average age of 5 members of a family is 21 yrs . if the age of the youngest child is 5 yrs find the average age of the family at the time of his birth​

Answer 1

Answer:-

Given:

Average age of a family of 5 members = 21 years.

Age of the youngest child = 5 yrs

We know that,

Average = sum of observations/Number of observations

Hence,

Sum of ages of 5 members (including child)/5 = 21

⟶ Sum of ages of 5 members = 21 * 5

⟶ Sum of ages of 5 members = 105 years

⟶ Sum of ages of 4 members + age of child = 105

⟶ Sum of ages of 4 members + 5 = 105

⟶ Sum of ages of 4 members = 100 years

Now,

⟶ Sum of ages of 4 members before 5 years = 100 - 4(5)

⟶ Sum of ages of 4 members before 5 years = 80 years

Hence,

⟶ Average age of the 4 members = 80/4

⟶ Average age of the 4 members = 20 years

Therefore, the average age of the family before the birth of the child was 20 years.

Answer 2

GIVEN :-

• Tʜᴇ ᴀᴠᴇʀᴀɢᴇ ᴀɢᴇ ᴏғ 5 ᴍᴇᴍʙᴇʀs ᴏғ ᴀ ғᴀᴍɪʟʏ ɪs 21 ʏᴇᴀʀs .

• Tʜᴇ ᴀɢᴇ ᴏғ ᴛʜᴇ ʏᴏᴜɴɢᴇsᴛ ᴄʜɪʟᴅ ɪs 5 ʏᴇᴀʀs .

TO FIND :-

• Tʜᴇ ᴀᴠᴇʀᴀɢᴇ ᴀɢᴇ ᴏғ ᴛʜᴇ ғᴀᴍɪʟʏ ᴀᴛ ᴛʜᴇ ᴛɪᴍᴇ ᴏғ ᴛʜᴇ ʙɪʀᴛʜ ᴏғ ᴛʜᴇ ʏᴏᴜɴɢᴇsᴛ ᴍᴇᴍʙᴇʀ .

SOLUTION :-

➪ Aᴛ ᴘʀᴇsᴇɴᴛ, ᴛʜᴇ ᴛᴏᴛᴀʟ ᴀɢᴇ ᴏғ ᴛʜᴇ ғᴀᴍɪʟʏ ɪs,

• 21 × 5 = 105 ʏᴇᴀʀs

☯︎ Wᴇ ʜᴀᴠᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ, ᴛʜᴇ ᴀɢᴇ ᴏғ ᴛʜᴇ ʏᴏᴜɴɢᴇsᴛ ᴄʜɪʟᴅ ɪs 5 ʏᴇᴀʀs .

☯︎ Hᴇɴᴄᴇ, ᴀᴛ ᴘʀᴇsᴇɴᴛ ᴛʜᴇ ᴛᴏᴛᴀʟ ᴀɢᴇ ᴏғ ᴛʜᴇ ʀᴇᴍᴀɪɴɪɴɢ ғᴀᴍɪʟʏ ᴍᴇᴍʙᴇʀs ɪs,

• 105 - 5 = 100 ʏᴇᴀʀs

☯︎ Nᴏᴡ, ᴛʜᴇ ᴛᴏᴛᴀʟ ᴀɢᴇ ᴏғ ᴛʜᴇ ʀᴇᴍᴀɪɴɪɴɢ ғᴀᴍɪʟʏ ᴍᴇᴍʙᴇʀs ᴅᴜʀɪɴɢ 5 ʏᴇᴀʀs ɪs,

• 4 × 5 = 20 ʏᴇᴀʀs

☯︎ Tʜᴇ ᴛᴏᴛᴀʟ ᴀɢᴇ ᴏғ ᴛʜᴇ ғᴀᴍɪʟʏ ᴀᴛ ᴛʜᴇ ᴛɪᴍᴇ ᴏғ ʙɪʀᴛʜ ᴏғ ᴛʜᴇ ʏᴏᴜɴɢᴇsᴛ ᴍᴇᴍʙᴇʀ ᴅᴜʀɪɴɢ 5 ʏᴇᴀʀs ᴀɢᴏ ɪs,

• 100 - 20 = 80 ʏᴇᴀʀs

$\red\therefore$ Tʜᴇ ᴀᴠᴇʀᴀɢᴇ ᴀɢᴇ ᴏғ ᴛʜᴇ ғᴀᴍɪʟʏ ᴀᴛ ᴛʜᴇ ᴛɪᴍᴇ ᴏғ ʙɪʀᴛʜ ᴏғ ᴛʜᴇ ʏᴏᴜɴɢᴇsᴛ ᴍᴇᴍʙᴇʀ ɪs,

$\red\checkmark\:\bf\purple{\dfrac{Total\:age\:of\:the\:family\:at\:the\:time\:of\:\atop{the\:birth\:of\:the\:of\:youngest\:member}}{Number\:of\:members\:in\:family\:at\:the\:\atop{time\:of\:birth\:of\:the\:youngest\:member}}\:}$

➳ 80/4

➳ 20 years

$\huge\red\therefore$ Tʜᴇ ᴀᴠᴇʀᴀɢᴇ ᴀɢᴇ ᴏғ ᴛʜᴇ ғᴀᴍɪʟʏ ᴀᴛ ᴛʜᴇ ᴛɪᴍᴇ ᴏғ ᴛʜᴇ ʙɪʀᴛʜ ᴏғ ᴛʜᴇ ʏᴏᴜɴɢᴇsᴛ ᴍᴇᴍʙᴇʀ ɪs "20 ʏᴇᴀʀs" .