- Let the M.P of the article be x.
- A discount of 30% was given on the M.P.
- So the selling price of the article (S.P) = M.P - Discount.
- Discount = 30% of x
[tex] = \frac{30}{100} x \\ = \frac{3x}{10} [/tex]
- Now S.P. = M.P - Discount
- or, S.P.
[tex] = x - \frac{3x}{10} \\ = \frac{10x - 3x}{10} \\ = \frac{7x}{10} [/tex]
- The shopkeeper loses Rs 400.
- Loss = C.P - S.P
- or, C.P = Loss + S.P.
- or, C.P = [tex]400 + \frac{7x}{10} \\ = \frac{4000 + 7x}{10} [/tex]
- Now if he allows 10% discount then the gain is Rs 200.
- Gain = S.P - C.P
- or, S.P = Gain + C.P
- S.P = [tex]200 + \frac{4000 + 7x}{10} \\ = \frac{6000 + 7x}{10} [/tex]
- Discount = 10 % of x [tex] = \frac{10}{100} x \\ = \frac{x}{10} [/tex]
- S.P. = M.P - Discount
- or, [tex] \frac{6000 + 7x}{10} = x - \frac{x}{10} \\ = > \frac{6000 + 7x}{10} = \frac{9x}{10} \\ = > 6000 + 7x = 9x \\ = > 9x - 7x = 6000 \\ = > 2x = 6000 \\ = > x = 3000[/tex]
- The M.P of the article is Rs 3000.
- C.P = [tex] \frac{4000 + 7x}{10} \\ = \frac {4000+7(3000)}{10} \\ = \frac{4000+21000}{10} \\ = 2500[/tex]
- The cost price is Rs 2500.
Answers:
Rs. 3000, Rs. 2500
Hope you could understand.
If you have any query, feel free to ask.
