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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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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 :-
![s = ( 1 - \frac{20}{100} ) \times m = 0.8m \\ \\ and \: c - s = 20](https://tex.z-dn.net/?f=s%20%3D%20%28%201%20-%20%20%5Cfrac%7B20%7D%7B100%7D%20%29%20%5Ctimes%20m%20%3D%200.8m%20%5C%5C%20%20%5C%5C%20and%20%5C%3A%20c%20%20-%20s%20%3D%2020)
C = 20 + 0.8 m ------------- eq 1
2) when shopkeeper sells at 20% discount then he makes a profit of 8% then we have
![s = ( 1 - \frac{10}{100} ) \times m = 0.9m \\ \\ and \\ \\ s = ( 1 + \frac{8}{100} ) \times c = \: \frac{0.9m}{1.08}](https://tex.z-dn.net/?f=s%20%3D%20%28%201%20-%20%20%5Cfrac%7B10%7D%7B100%7D%20%29%20%5Ctimes%20m%20%3D%200.9m%20%5C%5C%20%20%5C%5C%20and%20%20%5C%5C%20%20%5C%5C%20s%20%3D%20%28%201%20%20%2B%20%20%5Cfrac%7B8%7D%7B100%7D%20%29%20%5Ctimes%20c%20%3D%20%5C%3A%20%20%5Cfrac%7B0.9m%7D%7B1.08%7D%20)
since the cost price of bag doesn't change and equating 1 and 2 we get
![20 + 0.8m = \frac{0.9m}{1.08} \\ \\ 21.6 + 0.864m \: = 0.9m \\ \\ 0.036m \: = 21.6 \\ \\ m \: = 600](https://tex.z-dn.net/?f=20%20%2B%200.8m%20%3D%20%20%5Cfrac%7B0.9m%7D%7B1.08%7D%20%20%5C%5C%20%20%5C%5C%2021.6%20%2B%200.864m%20%5C%3A%20%20%3D%200.9m%20%5C%5C%20%20%5C%5C%200.036m%20%5C%3A%20%20%3D%2021.6%20%5C%5C%20%20%5C%5C%20m%20%5C%3A%20%20%3D%20600)
<h3>
hence ur answer is rupees 600</h3>
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