TWO NUMBERS ARE IN THE RATIO 5:6. IF 8 IS SUBTRACTED FROM BOTH THE NUMBERS THE RATIO BECOMES 4:5. FIND BOTH THE NUMBERS.
 

Asked by dalbirgolagarh | 22nd Jul, 2015, 03:59: PM

Expert Answer:

L e t space x space a n d space y space b e space t w o space n u m b e r s space s u c h space t h a t x over y equals 5 over 6 rightwards double arrow 6 x minus 5 y equals 0... left parenthesis 1 right parenthesis I f space 8 space i s space s u b t r a c t e d space f r o m space b o t h space t h e space n u m b e r s comma space t h e space r a t i o space i s space 4 colon 5 fraction numerator x minus 8 over denominator y minus 8 end fraction equals 4 over 5 rightwards double arrow 5 open parentheses x minus 8 close parentheses equals 4 open parentheses y minus 8 close parentheses rightwards double arrow 5 x minus 40 equals 4 y minus 32 rightwards double arrow 5 x minus 4 y equals 8.... left parenthesis 2 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 1 right parenthesis space b y space 4 space a n d space e q u a t i o n space left parenthesis 2 right parenthesis space b y space 5 comma space w e space h a v e comma 24 x minus 20 y equals 0... left parenthesis 3 right parenthesis 25 x minus 20 y equals 40... left parenthesis 4 right parenthesis S u b t r a c t i n g space e q u a t i o n space left parenthesis 3 right parenthesis space f r o m space left parenthesis 4 right parenthesis comma space w e space h a v e comma x equals 40 S u b s t i t u t i n g space t h e space v a l u e space x equals 40 space i n space e q u a t i o n space left parenthesis 1 right parenthesis comma space w e space h a v e comma 6 cross times 40 minus 5 y equals 0 rightwards double arrow 240 equals 5 y rightwards double arrow y equals 240 over 5 rightwards double arrow y equals 48 T h u s comma space t h e space n u m b e r s space a r e space 40 space a n d space 48.

Answered by Vimala Ramamurthy | 22nd Jul, 2015, 05:15: PM

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