Rajiv sold two chairs for Rs. 500 each. On one he gains 20% while on the other he loses 12%. Find his overall gain or loss percent?

Asked by Sushmita Dasgupta | 23rd Oct, 2015, 12:23: PM

Expert Answer:

S e l l i n g space p r i c e space o f space e a c h space c h a i r equals R s.500 G a i n space p e r c e n t a g e space o n space o n e space c h a i r equals 20 percent sign  S e l l l i n g space p r i c e equals C o s t space p r i c e plus g a i n space space space space space space space space space space space space space space space space space space space space equals C o s t space p r i c e plus 20 over 100 cross times C o s t space p r i c e L e t space x space b e space t h e space c o s t space p r i c e space o f space t h e space c h a i r. T h u s comma space 500 equals x plus 20 over 100 cross times x rightwards double arrow 500 equals x open parentheses 1 plus 20 over 100 close parentheses rightwards double arrow 500 equals x open parentheses 1 plus 1 fifth close parentheses rightwards double arrow 500 equals x open parentheses fraction numerator 5 plus 1 over denominator 5 end fraction close parentheses rightwards double arrow 500 equals fraction numerator 6 x over denominator 5 end fraction rightwards double arrow x equals 2500 over 6 L o s s space p e r c e n t a g e space o n space o n e space c h a i r equals 12 percent sign S e l l l i n g space p r i c e equals C o s t space p r i c e minus L o s s space space space space space space space space space space space space space space space space space space space space equals C o s t space p r i c e minus 12 over 100 cross times C o s t space p r i c e L e t space y space b e space t h e space c o s t space p r i c e space o f space t h e space c h a i r. T h u s comma space 500 equals y minus 12 over 100 cross times y rightwards double arrow 500 equals y open parentheses 1 minus 3 over 25 close parentheses rightwards double arrow 500 equals y open parentheses fraction numerator 25 minus 3 over denominator 25 end fraction close parentheses rightwards double arrow 500 equals y open parentheses 22 over 25 close parentheses rightwards double arrow 500 equals fraction numerator 22 y over denominator 25 end fraction rightwards double arrow y equals 12500 over 22 rightwards double arrow y equals 6250 over 11 T o t a l space cos t space p r i c e space o f space t h e space c h a i r s equals x plus y 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 space space space space space space space space space space space space space space space space space space space equals 2500 over 6 plus 6250 over 11 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 space space space space space space space space space space space space space space space space space space space equals fraction numerator 27500 plus 37500 over denominator 66 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 space space space space space space space space space space space space space space space space space space space equals 65000 over 66 T o t a l space s e l l i n g space p r i c e equals 500 plus 500 equals 1000 T o t a l space S e l l i n g space p r i c e less than T o t a l space C o s t space p r i c e space a n d space h e n c e space t h e r e space i s space a space l o s s. L o s s equals 1000 minus 65000 over 66 space space space space space space space equals fraction numerator 66000 minus 65000 over denominator 66 end fraction space space space space space space space equals 1000 over 66 L o s s space p e r c e n t a g e equals fraction numerator L o s s over denominator C o s t space p r i c e end fraction cross times 100 percent sign 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 space equals fraction numerator 1000 over 66 over denominator 65000 over 66 end fraction cross times 100 percent sign 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 space equals 1 over 65 cross times 100 percent sign 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 space equals 1 35 over 65 percent sign 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 space equals 1 7 over 13 percent sign

Answered by Vimala Ramamurthy | 23rd Oct, 2015, 02:46: PM