1.

Successive discounts of a% and b% on the marked price of an article is equivalent to a single discount of:1). \(\left( {a - b\; + \;\frac{{ab}}{{100}}} \right)\% \)2). \(\left( {a - b - \frac{{ab}}{{100}}} \right)\%\)3). \(\left( {a\; + \;b - \frac{{ab}}{{100}}} \right)\%\)4). \(\left( {a\; + \;b\; + \;\frac{{ab}}{{100}}} \right)\%\)

Answer»

Let the marked PRICE of the ARTICLE be RS. p

Selling Price when discount of a% is given = [(100 - a)/100] × p

Selling price when discount of b% is given on the above selling price

= [(100 - b)/100] × [(100 - a)/100] × p

= [(100 - b) × (100 - a)]/10000 × p

Now consider a single discount of c% is given on the product.

⇒ Selling price of the product = [(100 - c)/100] × p

⇒ [(100 - b) × (100 - a)]/10000 × p = [(100 - c)/100] × p

⇒ (100 - b) × (100 - a)/10000 = (100 - c)/100

⇒ (100 - b) × (100 - a)/100 = (100 - c)

⇒ (100 – a) × (100 – b) = (100 – c) × 100

⇒ 10000 – 100B – 100a + ab = 10000 – 100c

⇒ 100c = 100a + 100b – ab

⇒ c = [a + b – (ab/100)]%


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