[1000] A trader gives 12% additional discount on the discounted price, after giving an initial discount of

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A trader gives 12% additional discount on the discounted price, after giving an initial discount of 20% on the labeled price of an item. The final sale price of the item is Rs.704. Find out the labeled price?

1000

2000

1200

920

Explanation:

Let the labeled price = $x$

SP = 704

Initial Discount = 20%

Price after initial discount = $x \times \dfrac{80}{100}$

Additional discount = 12%

Price after additional discount= $x \times \dfrac{80}{100}\times \dfrac{88}{100}$

But Price after additional discount = SP = 704

$\Rightarrow x \times \dfrac{80}{100}\times \dfrac{88}{100}$ = 704

$\Rightarrow x \times \dfrac{4}{5}\times \dfrac{22}{25} $= 704

$\Rightarrow x = 704 \times \dfrac{25}{22}\times \dfrac{5}{4} = 176 \times \dfrac{25}{22}\times 5 $

= $8 \times 25 \times 5 = 40 \times 25$ = 1000

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