Question

22. Two taps can fill a tub in 24 and 32 minutes, respectively. The drain can empty the full tub in 16 mins.
If they are opened together at the same time, how long will it take for the tub to be full?
WRITE ANSWER PHOTO​

Answer 1

$\rm\underline\bold{Question \purple{\huge{\checkmark}}}$

Two taps can fill a tub in 24 and 32 minutes, respectively. The drain can empty the full tub in 16 mins.

If they are opened together at the same time, how long will it take for the tub to be full?

$\huge{\tt{\colorbox{aqua}{AnswEr:}}}$

Part filled by A in 1 min = 124124

Part filled by B in 1 min = 132132

Let B is closed after x min. Then, [Part filled by (A + B) in x min] + [Part filled by A in (9-x) min] = 1

Therefore,

x(124+132)+(9−x)×124=1x(124+132)+(9−x)×124=1

=> x(4+396)+(9−x)24=1x(4+396)+(9−x)24=1

=> 7x96+(9−x)24=17x96+(9−x)24=1

=> 7x+4(9−x)96=17x+4(9−x)96=1

=> 7x+4(9−x)=967x+4(9−x)=96

=> 7x+36-4x=96

=> 7x - 4x = 96 - 36

= 3x = 60 => x = 603603 = 20

Hence, B must be closed after 20 min.

Answer 2

Part filled by A in 1 min = 124124

Part filled by B in 1 min = 132132

Let B is closed after x min. Then, [Part filled by (A + B) in x min] + [Part filled by A in (9-x) min] = 1

Therefore,

x(124+132)+(9−x)×124=1x(124+132)+(9−x)×124=1

=> x(4+396)+(9−x)24=1x(4+396)+(9−x)24=1

=> 7x96+(9−x)24=17x96+(9−x)24=1

=> 7x+4(9−x)96=17x+4(9−x)96=1

=> 7x+4(9−x)=967x+4(9−x)=96

=> 7x+36-4x=96

=> 7x - 4x = 96 - 36

= 3x = 60 => x = 603603 = 20

Hence, B must be closed after 20 min.