JOHN ORDERED 4 PAIRS OF BLACK SOCKS AND SOME ADDITIONAL PAIRS OF BLUE SOCKS.THE PRICE OF THE BLACK SOCKS PER PAIR WAS TWICE THAT OF THE BLUE.WHEN THE ORDER WAS FILLED,IT WAS FOUND THAT THE NUMBER OF PAIRS OF THE TWO COLOURS HAD BEEN INTER CHANGED.THIS INCREASED THE BILL BY 50 PERCENT.WHAT WAS THE RATIO OF THE NUMBER OF PAIRS OF BLACK SOCKS TO THE NUMBER OF PAIRS OF BLUE SOCKS IN YHE ORIGINAL ORDER. 

Asked by M.s.srinidhi21 | 28th Sep, 2014, 11:22: PM

Expert Answer:

L e t space t h e space r a t e space o f space b l a c k space s o c k s space equals R s. x L e t space t h e space r a t e space o f space b l u e space s o c k s equals R s. y G i v e n space t h a t space x equals 2 y L e t space k space b e space t h e space n u m b e r space o f space b l u e space s o c k s space J o h n space i n t e n d space t o space b u y. T h e space t o t a l space a m o u n t space h e space i n t e n d e d space t o space p a y equals 4 x plus k y equals 4 x plus k open parentheses x over 2 close parentheses I n t e r c h a n g e d space b i l l equals k x plus 4 y equals k x plus 4 open parentheses x over 2 close parentheses equals k x plus 2 x G i v e n space t h a t space t h e space b i l l space h a s space b e e n space i n t e r c h a n g e d space a n d space h e n c e space t h e space cos t space h a s space b e e n space i n c r e a s e space b y space 50 %. rightwards double arrow k x plus 2 x equals 3 over 2 open square brackets 4 x plus k open parentheses x over 2 close parentheses close square brackets rightwards double arrow 2 k x plus 4 x equals 12 x plus fraction numerator 3 k x over denominator 2 end fraction rightwards double arrow 2 k minus fraction numerator 3 k over denominator 2 end fraction equals 12 minus 4 rightwards double arrow k over 2 equals 8 rightwards double arrow k equals 16 T h u s comma space t h e space r a t i o space o f space n u m b e r space o f space p a i r s space o f space b l a c k space s o c k s space t o space t h e space n u m b e r space o f space p a i r s space o f space b l u e space s o c k s equals 4 over 16 equals 1 fourth.

Answered by Vimala Ramamurthy | 29th Sep, 2014, 10:22: AM

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