Please solve this

Asked by aastharoy997 | 26th Mar, 2020, 01:28: PM

Expert Answer:

A vegetable vendor bought some mangoes and sold one third of them at a gain of 25%, one-fifth of the total mangoes at a loss of 25% and the rest being spoiled were thrown away. Find his percentage of loss on the whole.
Solution:-
Let the number of mangoes bought be 100.
O n e minus t h i r d space o f space t h e space m a n g o e s space equals space 100 over 3
O n e minus f i f t h space o f space t h e space t o t a l space m a n g o e s space equals space 100 over 5
L e t space t h e space C P space o f space e a c h space m a n g o space b e space x space R s.
S P space o f space o n e minus t h i r d space o f space m a n g o e s space equals space fraction numerator 100 x over denominator 3 end fraction open parentheses 1 plus 25 over 100 close parentheses space a s space t h e r e space i s space g a i n space o f space 25 percent sign
S P space o f space o n e minus f i f t h space o f space m a n g o e s space equals space fraction numerator 100 x over denominator 5 end fraction open parentheses 1 minus 25 over 100 close parentheses space a s space t h e r e space i s space l o s space o f space 25 percent sign
T h e space r e m a i n i n g space m a n g o e s space equals space 100 minus 100 over 3 minus 100 over 5 equals 100 over 7
S P space o f space t h e s e space m a n g o e s space i s space R s. space 0 space a s space t h e y space g o t space s p o i l e d
T o t a l space S P equals fraction numerator 100 x over denominator 3 end fraction open parentheses 1 plus 25 over 100 close parentheses plus fraction numerator 100 x over denominator 5 end fraction open parentheses 1 minus 25 over 100 close parentheses plus 0
equals 125 over 100 cross times fraction numerator 100 x over denominator 3 end fraction plus 75 over 100 cross times fraction numerator 100 x over denominator 5 end fraction
equals fraction numerator 170 x over denominator 3 end fraction
L o s s equals C P minus S P equals 100 x minus fraction numerator 170 x over denominator 3 end fraction equals fraction numerator 130 x over denominator 3 end fraction
L o s s space percent sign equals fraction numerator begin display style fraction numerator 130 x over denominator 3 end fraction end style over denominator 100 x end fraction cross times 100 equals 130 over 3 equals 43 1 third percent sign

Answered by Renu Varma | 27th Mar, 2020, 10:58: AM

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