Question

A water tap A takes seven minutes more than water tap B for filling up a tank with water. The tap A takes 16 minutes more than time taken by both the taps together to fill the tank. Find the each time the would take alone to fill the tank.

Answer 1

Let the Water tap B takes the time to fill the tank = y minutes

Now according o 1st condition

The Water tap A takes the time to fill the tank = (y + 7) minutes

Also according to second condition

Time taken by Tap A + 16 = Time taken by Both the taps

                    y + 7 + 16       =     y  + ( y + 7 )  

                    y  + 23           =  2 y  +  7    

             Rearranging the above equation, we get    

               2 y + 7      =  y + 23  

                2 y  -   y   = 23 - 7    

                     y    =    16  

So Water tap B takes the time to fill the tank = 16 minutes

And

Water tap A takes the time to fill the tank = 16 + 7 = 23  minutes

So Tap B alone takes 16 minutes and Tap A alone takes 23 minutes to fill the tank.

Answer 2

ʟᴇᴛ ᴛʜᴇ ᴛɪᴍᴇ ᴛᴀᴋᴇɴ ʙʏ ᴀ ɪꜱ x ᴍɪɴᴜᴛᴇꜱ ᴀɴᴅ ʙ ɪꜱ ʏ ᴍɪɴᴜᴛᴇꜱ,

ʜᴇɴᴄᴇ ꜰʀᴏᴍ ᴛʜᴇ 1ꜱᴛ ꜱᴛᴀᴛᴇᴍᴇɴᴛ ᴡᴇ ʜᴀᴠᴇ,

x-ʏ = 7 = > ʏ = x-7..........................ᴇQ1

ɴᴏᴡ, ɪɴ ᴏɴᴇ ᴍɪɴᴜᴛᴇ ᴛᴀɴᴋ ꜰɪʟʟᴇᴅ ʙʏ ᴀ = 1/x

ᴀɴᴅ  ɪɴ ᴏɴᴇ ᴍɪɴᴜᴛᴇ ᴛᴀɴᴋ ꜰɪʟʟᴇᴅ ʙʏ ʙ = 1/ʏ

ꜱᴏ ᴄᴏᴍʙɪɴᴇ ᴛᴏɢᴇᴛʜᴇʀ ʙᴏᴛʜ ᴄᴀɴ ꜰɪʟʟ = 1/x  + 1/ʏ ᴛᴀɴᴋ ɪɴ ᴏɴᴇ ᴍɪɴᴜᴛᴇ,

ʜᴇɴᴄᴇ ᴛɪᴍᴇ ᴛᴀᴋᴇɴ ʙʏ ʙᴏᴛʜ ᴛʜᴇ ᴛᴀᴘꜱ ᴛᴏ ꜰɪʟʟ ᴛʜᴇ ᴛᴀɴᴋ

= 1/(1/x + 1/ʏ)

= xʏ/x+ʏ

ɴᴏᴡ ꜰʀᴏᴍ ᴛʜᴇ ꜱᴇᴄᴏɴᴅ ꜱᴛᴀᴛᴇᴍᴇɴᴛ,

x- xʏ/x+ʏ   = 16

=> x² + xʏ - xʏ = 16(x+ʏ)

=> x² -16x - 16ʏ = 0

ᴘᴜᴛᴛɪɴɢ ᴛʜᴇ ᴠᴀʟᴜᴇ ᴏꜰ ʏ ꜰʀᴏᴍ ᴇQ1

x²-16x - 16(x-7) = 0

=> x² - 32x + 112 = 0.

ꜱᴏʟᴠɪɴɢ ᴛʜᴇ ᴀʙᴏᴠᴇ Qᴜᴀᴅʀᴀᴛɪᴄ ᴇQɴ, ᴡᴇ ɢᴇᴛ

x = 28 ᴏʀ 4

ʀᴇᴊᴇᴄᴛɪɴɢ 4 ᴀꜱ x ᴄᴀɴ'ᴛ ʙᴇ ʟᴇꜱꜱ ᴛʜᴀɴ 7

x = 28

ʏ = x-7 = 28-7 = 21

ʜᴇɴᴄᴇ ᴛɪᴍᴇ ᴛᴀᴋᴇɴ ʙʏ ʙᴏᴛʜ ᴛʜᴇ ᴛᴀᴘꜱ ᴀʀᴇ 28 ᴀɴᴅ 21 ᴍɪɴᴜᴛᴇꜱ ᴀʟᴏɴᴇ.