Question

C) 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.

help!!​

Answer 1

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`\Large\fbox{\color{purple}{QUESTION}}`

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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`\Large\fbox{\color{purple}{ SOLUTION }}`

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 - (20)/(100) ) * m = 0.8m \\ \\ and \: c - s = 20`

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 - (10)/(100) ) * m = 0.9m \\ \\ and \\ \\ s = ( 1 + (8)/(100) ) * c = \: (0.9m)/(1.08)`

since the cost price of bag doesn't change and equating 1 and 2 we get

`20 + 0.8m = (0.9m)/(1.08) \\ \\ 21.6 + 0.864m \: = 0.9m \\ \\ 0.036m \: = 21.6 \\ \\ m \: = 600`

hence ur answer is rupees 600

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Answer 2

Answer: Marked price Rs. 600

Explanation:

Let M be the marked price

1) When shop keeper sold at 20% discount, ie. SP = 0.8M

CP - SP = 20

CP = 20 + SP

CP = 20 + 0.8M

2) When shopkeeper sells at 8% discount, he makes a profit of 10%

SP = 0.9M/1.08

Equating 1 and 2, we get

20 + 0.8M = 0.9M/1.08

21.6 + 0.864M = 0.9M

0.036 M = 21.6

M = 21.6 / 0 036

M = 600