Question

Pipe A and B can fill an empty tank in 10 hours and 15 hours respectively. If both are opened together in the empty tank, how much time will they take to fill it completely? ​

Answer 1

$\huge \underline \textcolor{teal}{solvation : }$

ǫᴜᴇsᴛɪᴏɴ : Pipe A and B can fill an empty tank in 10 hours and 15 hours respectively. If both are opened together in the empty tank, how much time will they take to fill it completely?

ᴀɴsᴡᴇʀ

ʟᴇᴛ ᴛʜᴇ ᴛᴀɴᴋ ʙᴇ ғɪʟʟᴇᴅ ᴜᴘ ɪɴ x ʜʀs

ᴘɪᴘᴇ ᴀ ᴄᴀɴ ғɪʟʟ ᴀ ᴛᴀɴᴋ ɪɴ 10 ʜʀs

ᴛʜᴜs ᴀᴍᴏᴜɴᴛ ғɪʟʟᴇᴅ ʙʏ ᴘɪᴘᴇ ᴀ ɪs x/10

ᴘɪᴘᴇ ʙ ᴄᴀɴ ғɪʟʟ ᴀ ᴛᴀɴᴋ ɪɴ 15 ʜʀs

ᴛʜᴜs ᴀᴍᴏᴜɴᴛ ғɪʟʟᴇᴅ ʙʏ ᴘɪᴘᴇ ʙ ɪs x/15

ᴡʜᴇɴ ᴛʜᴇ ᴛᴀɴᴋ ʙᴇᴄᴏᴍᴇ ғᴜʟʟ ᴍᴇᴀɴ [100] ᴛʜᴇ ᴇǫᴜᴀᴛɪᴏɴ ᴄᴀɴ ʙᴇ ᴅᴇʙɪᴛᴇᴅ ᴀs

x/10 - x/15 = 100 % ᴏʀ 100/100

(3x-2x)/30 = 100/100

100x = 30 × 100

x = 3000/100

x = 3 ʜʀs

ᴛʜᴜs ᴛᴀɴᴋ ᴄᴏᴜʟᴅ ʙᴇ ғɪʟʟᴇᴅ ᴜᴘ ɪɴ 30 ʜʀs ᴀʟᴛᴏɢᴇᴛʜᴇʀ ✓

ᴀɴsᴡᴇʀ ʙʏ

ᴄᴀɴᴅʏʙʟᴜsʜ

❤️

Answer 2

Answer:

Pipe A can fill the tank in

10

hours

A's one hour's work

=

1

10

Pipe B can fill the tank in

15

hours.

B's one hour's work

=

1

15

∴

A and B's one hour's work

=

1

10

+

1

15

=

1

×

3

10

×

3

+

1

×

2

15

×

2

[L.C.M of

10

and

15

is

30

]

=

3

30

+

2

30

=

3

+

2

30

=

5

30

=

1

6

∴

A's and B's one hour's work

=

1

6

∴

Pipes A and B can fill the empty tank in

6

hours.