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CBSE Class 10 Answered

two vessels A and B contain spirit and water  in the ratio 5/2 and 7/6 respectively.find the ratio in which these mixture be mixed to obtain a new mixture in vessel C containing spirit and water in the ratio 8/5
Asked by apurva151 | 14 Dec, 2015, 06:42: PM
answered-by-expert Expert Answer
Q u a n t i t t y space o f space s p i r i t space i n space 1 space l i t r e space i n space v e s s e l space A equals fraction numerator 5 over denominator 5 plus 2 end fraction equals 5 over 7 space l i t r r e Q u a n t i t y space o f space s p i r i t space i n space 1 space l i t r e space i n space v e s s e l space B equals fraction numerator 7 over denominator 7 plus 6 end fraction equals 7 over 13 space l i t r e R e q u i r e d space q u a n t i t y space o f space s p i r i t space i n space 1 space l i t r e space i n space v e s s e l space C equals fraction numerator 8 over denominator 8 plus 5 end fraction equals 8 over 13 space l i t r e I f space t w o space i n g r e d i e n t s space A space a n d space B space o f space p r i c e space x space a n d space y space r e s p e c t i v e l y space a r e space m i x e d space a n d space t h e space p r i c e space o f space r e s u l tan t space m i x t u r e space i s space M space left parenthesis m e a n space p r i c e right parenthesis t h e n space t h e space r a t i o space left parenthesis R right parenthesis space i n space w h i c h space i n g r e d i e n t s space a r e space m i x e d space i s space g i v e n space b y comma space t h e space r u l e space o f space a l l e g a t i o n space space R equals fraction numerator M minus y over denominator x minus M end fraction T h u s space b y space t h e space r u l e space o f space a l l e g a t i o n comma space w e space h a v e comma R e q u i r e d space R a t i o equals fraction numerator 8 over 13 minus 7 over 13 over denominator 5 over 7 minus 8 over 13 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator begin display style 1 over 13 end style over denominator begin display style fraction numerator 65 minus 56 over denominator 91 end fraction end style end fraction space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator begin display style 1 over 13 end style over denominator begin display style 9 over 91 end style end fraction space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator begin display style 7 end style over denominator begin display style 9 end style end fraction space T h e space r a t i o space i n space w h i c h space t h e s e space m i x t u r e space b e space m i x e d space t o space o b t a i n space a space n e w space m i x t u r e space i n space v e s s e l space C space i n space t h e space r e q u i r e d space r a t i o space i s space 7 colon 9.
Answered by Vimala Ramamurthy | 15 Dec, 2015, 10:25: AM

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