Answer:
[tex]\boxed{\sf \: \: Single\:discount = 24 \: \% \: }\\ [/tex]
Step-by-step explanation:
Let assume that Marked price of an article be Rs 100.
Given that, two successive discounts of 20% and 5% are applicable on article.
We know, Marked price, Selling price and successive discounts of x% and y% are connected by the relationship
[tex]\sf \: \boxed{\sf \: Selling \: price = Marked \: price\left(1 - \dfrac{x}{100} \right)\left(1 - \dfrac{y}{100} \right) \: } \\ [/tex]
So, on substituting the values, we get
[tex]\sf \: Selling \: price = 100\left(1 - \dfrac{20}{100} \right)\left(1 - \dfrac{5}{100} \right) \: \\ [/tex]
[tex]\sf \: Selling \: price = 100\left(1 - \dfrac{1}{5} \right)\left(1 - \dfrac{1}{20} \right) \: \\ [/tex]
[tex]\sf \: Selling \: price = 100\left( \dfrac{5 - 1}{5} \right)\left(\dfrac{20 - 1}{20} \right) \: \\ [/tex]
[tex]\sf \: Selling \: price = 4 \times 19 \: \\ [/tex]
[tex]\implies\sf \: Selling \: price = Rs \: 76 \: \\ [/tex]
Now, We have
[tex]\sf \: Marked \: price \: = \: Rs \: 100 \\ [/tex]
[tex]\sf \: Selling \: price \: = \: Rs \: 76 \\ [/tex]
Now, We know
Marked price, Selling price and Discount % are connected by the relationship
[tex]\sf \: Discount\% = \dfrac{Marked \: price - Selling \: price}{Marked \: price} \times 100 \\ [/tex]
[tex]\sf \: Discount\% = \dfrac{100 - 76}{100} \times 100 \\ [/tex]
[tex]\implies\sf \: Discount\% = 24 \\ [/tex]
Hence,
[tex]\implies\sf \: Single\:discount = 24 \: \%\\ \\ [/tex]
[tex]\rule{190pt}{2pt}[/tex]
Short Cut Method
Marked price(MP), Single discount and successive discounts of x% and y% are connected by the relationship
[tex]\sf \: \boxed{\sf \: Single\:discount\% = MP - MP\left(1 - \dfrac{x}{100} \right)\left(1 - \dfrac{y}{100} \right) \: } \\ [/tex]
Or
[tex]\sf \: \boxed{\sf \: Single\:discount\% = MP - MP\left( \dfrac{100 - x}{100} \right)\left(\dfrac{100 - y}{100} \right) \: } \\ [/tex]
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Verified answer
Answer:
[tex]\boxed{\sf \: \: Single\:discount = 24 \: \% \: }\\ [/tex]
Step-by-step explanation:
Let assume that Marked price of an article be Rs 100.
Given that, two successive discounts of 20% and 5% are applicable on article.
We know, Marked price, Selling price and successive discounts of x% and y% are connected by the relationship
[tex]\sf \: \boxed{\sf \: Selling \: price = Marked \: price\left(1 - \dfrac{x}{100} \right)\left(1 - \dfrac{y}{100} \right) \: } \\ [/tex]
So, on substituting the values, we get
[tex]\sf \: Selling \: price = 100\left(1 - \dfrac{20}{100} \right)\left(1 - \dfrac{5}{100} \right) \: \\ [/tex]
[tex]\sf \: Selling \: price = 100\left(1 - \dfrac{1}{5} \right)\left(1 - \dfrac{1}{20} \right) \: \\ [/tex]
[tex]\sf \: Selling \: price = 100\left( \dfrac{5 - 1}{5} \right)\left(\dfrac{20 - 1}{20} \right) \: \\ [/tex]
[tex]\sf \: Selling \: price = 4 \times 19 \: \\ [/tex]
[tex]\implies\sf \: Selling \: price = Rs \: 76 \: \\ [/tex]
Now, We have
[tex]\sf \: Marked \: price \: = \: Rs \: 100 \\ [/tex]
[tex]\sf \: Selling \: price \: = \: Rs \: 76 \\ [/tex]
Now, We know
Marked price, Selling price and Discount % are connected by the relationship
[tex]\sf \: Discount\% = \dfrac{Marked \: price - Selling \: price}{Marked \: price} \times 100 \\ [/tex]
[tex]\sf \: Discount\% = \dfrac{100 - 76}{100} \times 100 \\ [/tex]
[tex]\implies\sf \: Discount\% = 24 \\ [/tex]
Hence,
[tex]\implies\sf \: Single\:discount = 24 \: \%\\ \\ [/tex]
[tex]\rule{190pt}{2pt}[/tex]
Short Cut Method
Marked price(MP), Single discount and successive discounts of x% and y% are connected by the relationship
[tex]\sf \: \boxed{\sf \: Single\:discount\% = MP - MP\left(1 - \dfrac{x}{100} \right)\left(1 - \dfrac{y}{100} \right) \: } \\ [/tex]
Or
[tex]\sf \: \boxed{\sf \: Single\:discount\% = MP - MP\left( \dfrac{100 - x}{100} \right)\left(\dfrac{100 - y}{100} \right) \: } \\ [/tex]