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[tex]\bf\Huge\red{\mid{\overline{\underline{ ANSWER }}}\mid } [/tex]
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[tex]\Large\fbox{\color{purple}{QUESTION}}[/tex]
A shopkeeper made a loss of Rs 20 when he sold a bag at 20% discount. If he had sold it at 10% discount, he would have gained 8%. Find the marked price of the bag.
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[tex]\Large\fbox{\color{purple}{ SOLUTION }}[/tex]
let M, S and C be the mark price, selling price & cost price respectively.
1) when shopkeeper sells at 20% discount then he suffers a loss of rupees 20 then we have :-
[tex]s = ( 1 - \frac{20}{100} ) \times m = 0.8m \\ \\ and \: c - s = 20[/tex]
C = 20 + 0.8 m ------------- eq 1
2) when shopkeeper sells at 20% discount then he makes a profit of 8% then we have
[tex]s = ( 1 - \frac{10}{100} ) \times m = 0.9m \\ \\ and \\ \\ s = ( 1 + \frac{8}{100} ) \times c = \: \frac{0.9m}{1.08} [/tex]
since the cost price of bag doesn't change and equating 1 and 2 we get
[tex]20 + 0.8m = \frac{0.9m}{1.08} \\ \\ 21.6 + 0.864m \: = 0.9m \\ \\ 0.036m \: = 21.6 \\ \\ m \: = 600[/tex]
hence ur answer is rupees 600
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