CBSE Class 10 Answered

It Takes 12 hrs to fil a swimming pool using two pipes . I f the pipe of larger diameter is used for 4 hrs and the pipe of smaller diameter for 9 hrs , only half the pool can be filled . How long would it take for each pipe to fill the pool separately ?

Asked by Aadyasha | 05 Sep, 2015, 12:07: PM

Expert Answer

$L e t space A space a n d space B space a r e space t h e space t w o space p i p i e s. T h u s comma space t h e space q u a n t i t y space o f space w a t e r space f i l l e d space b y space t h e space p i p e space A space i n space o n e space h o u r space i s space 1 over A space a n d space b y space t h e space p i p e space i s space 1 over B T h u s comma space i n space 1 space h o u r space t h e space q u a n t i t y space o f space w a t e r space f i l l e d space b y space b o t h space t h e space p i p e s space i s space 1 over A plus 1 over B I t space t a k e s space 12 space h o u r s space t o space f i l l space t h e space p o o l space f o r space b o t h space t h e space p i p e s. H e n c e comma space w e space h a v e comma 1 over A plus 1 over B equals 1 over 12... left parenthesis 1 right parenthesis I n space 4 space h o u r s space t h e space q u a n t i t y space o f space w a t e r space f i l l e d space b y space p i p e space A space i s space 4 over A. A n d space i n space 9 space h o u r s space t h e space q u a n t i t y space o f space w a e r space f i l l e d space b y space p i p e space B space i s space 9 over B F r o m space t h e space g i v e n space s t a t e m e n t comma space w e space h a v e comma 4 over A plus 9 over B equals 1 half... left parenthesis 2 right parenthesis R e w r i t i n g space t h e space e q u a t i o o n s space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis comma space w e space h a v e comma x plus y equals 1 over 12... left parenthesis 3 right parenthesis 4 x plus 9 y equals 1 half... left parenthesis 4 right parenthesis M u l t i p l y i n g space e q u a t i o n space left parenthesis 3 right parenthesis space b y space 4 space a n d space s u b t r a c t i n g space f r o m space e q u a t i o n space left parenthesis 3 right parenthesis comma space w e space h a v e comma 4 x plus 9 y equals 1 half 4 x plus 4 y equals 1 third T h u s comma space w e space h a v e comma 5 y equals 1 half minus 1 third rightwards double arrow 5 y equals 1 over 6 rightwards double arrow y equals 1 over 30 rightwards double arrow B equals 30 T h u s comma space i f space t h e space s e c o n d space p i p e space a l o n e space f i l l s space t h e space p o o l space i t space w i l l space t a k e space 30 space h o u r s. S u b s t i t u t i n g space t h e space v a l u e space y equals 1 over 30 space i n space e q u a t i o n space left parenthesis 3 right parenthesis comma space w e space h a v e comma x equals 1 over 12 minus 1 over 30 space space space equals fraction numerator 5 minus 2 over denominator 60 end fraction space space space equals 3 over 60 space space space equals 1 over 20 rightwards double arrow A equals 20 therefore I f space t h e space f i r s t space p i p e space a l o n e space f i l l s space t h e space p o o l space i t space w i l l space t a k e space 20 space h o u r s.$