Question

It can take 12 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for
4 hours and the pipe of smaller diameter for 9 hours, only half the pool can be filled. How long would
it take for each pipe to fill the pool separately?
[NCERT Exemplar]



at image of the work pleaseeee​

Answer 1

Answer:

let larger pipe can fill pool separately in x hrs

let smaller pipe can fill pool separately in y hrs

pool filled by larger pipe in 1 hr=1/x

pool filled by larger pipe in 4 hr=4/x

pool filled by smaller pipe in 1 hr=1/y

pool filled by smaller pipe in 9 hr=9/y

4/x+9/y = .5

4y+9x=.5xy----------1

pool filled by larger pipe in 12 hr=12/x

pool filled by smaller pipe in 12 hr=12/y

12/x+12/y=1

12x+12y=xy

put value of xy in equation 1

9x+4y=6x+6y

3x=2y

y=1.5x

so exact value of filling is not possible to determine but but from the final equation we can conclude that time taken by smaller pipe is 1.5 times time taken by larger pipe

for example If larger pipe can fill the pool in 2 hrs then smaller pipe will take 3 hrs to fill the pool separately