Question

Q.28. A alone can do a work in 4 days and B alone can do a work in 6 days. How much time would they take if they work together? *​

Answer 1

Answer:

The number of days taken by two individuals is given in the question and we have to find the total number of days they will take to complete work together.

GiveN:

• Time taken by A = 4 days
• Time taken by B = 6 days

To find the time taken when they work together...?

Solution:

1 day's work of A = 1/4

1 day's work of B = 1/6

If they work together, there one day work would be:

➝ 1/4 + 1/6

➝ 4 + 6/24

➝ 10/24

➝ 5/12

So, In one day A and B can complete 5/12 of the work, So total number of days taken by them to complete together:

$\large{ \boxed{ \red{ \bf{ \frac{12}{5} = 2.4 \: days}}}}$

And we are done !!

Answer 2

GIVEN :-

• A ᴀʟᴏɴᴇ ᴄᴀɴ ᴅᴏ ᴀ ᴡᴏʀᴋ ɪɴ 4 ᴅᴀʏs .

• B ᴀʟᴏɴᴇ ᴄᴀɴ ᴅᴏ ᴀ ᴡᴏʀᴋ ɪɴ 6 ᴅᴀʏs .

TO FIND :-

• Tʜᴇ ᴛɪᴍᴇ ᴛʜᴇʏ ᴡᴏᴜʟᴅ ᴛᴀᴋᴇ ɪғ ᴛʜᴇʏ ᴡᴏʀᴋ ᴛᴏɢᴇᴛʜᴇʀ .

SOLUTION :-

ʟᴇᴛ,

• Tʜᴇ ᴛᴏᴛᴀʟ ᴡᴏʀᴋ = 1

Fᴏʀ 'A' :-

➪ A ᴄᴀɴ ᴀʟᴏɴᴇ ᴅᴏ ᴛʜᴇ 1 ᴡᴏʀᴋ ɪɴ 4 ᴅᴀʏs .

☯︎ Sᴏ, ɪɴ ᴏɴᴇ ᴅᴀʏ A ᴄᴀɴ ᴅᴏ = $\bf\red{\dfrac{1}{4}}$ ᴡᴏʀᴋ .

Fᴏʀ 'B' :-

➪ B ᴄᴀɴ ᴀʟᴏɴᴇ ᴅᴏ ᴛʜᴇ 1 ᴡᴏʀᴋ ɪɴ 6 ᴅᴀʏs .

☯︎ Sᴏ, ɪɴ ᴏɴᴇ ᴅᴀʏ B ᴄᴀɴ ᴅᴏ = $\bf\red{\dfrac{1}{6}}$ ᴡᴏʀᴋ .

Fᴏʀ ʙᴏᴛʜ 'A' ᴀɴᴅ 'B' :-

➪ ʟᴇᴛ, A ᴀɴᴅ B ᴛᴏɢᴇᴛʜᴇʀ ᴅᴏ ᴛʜᴇ 1 ᴡᴏʀᴋ ɪɴ X ᴅᴀʏs .

☯︎ Sᴏ, ɪɴ ᴏɴᴇ ᴅᴀʏ A ᴀɴᴅ B ᴄᴀɴ ᴅᴏ = $\bf\red{\dfrac{1}{X}}$ ᴡᴏʀᴋ .

$\bf{:\implies\:\dfrac{1}{4}\:+\:\dfrac{1}{6}\:=\:\dfrac{1}{X}\:}$

$\rm{:\implies\:\dfrac{3\:+\:2}{12}\:=\:\dfrac{1}{X}\:}$

$\rm{:\implies\:\dfrac{5}{12}\:=\:\dfrac{1}{X}\:}$

$\bf\green{:\implies\:X\:=\:\dfrac{12}{5}\:}$

➳ X = 12/5 = 2.4 Days .

$\huge\red\therefore$ Tʜᴇ ᴛɪᴍᴇ ᴛʜᴀᴛ ʙᴏᴛʜ A ᴀɴᴅ B ᴡᴏᴜʟᴅ ᴛᴀᴋᴇ ɪғ ᴛʜᴇʏ ᴡᴏʀᴋ ᴛᴏɢᴇᴛʜᴇʀ ɪs "2.4 ᴅᴀʏs" .