Answer:

[tex]\qquad \:\boxed{\begin{aligned}& \qquad \:\sf \:(1) \: \: 20\% \: above \: the \:cost \: price\qquad \: \\ \\& \qquad \:\sf \:(2) \: \: Discount\% \: = \: 24 \end{aligned}} \qquad \: \\ \\ [/tex]

Step-by-step explanation:

[tex]\large\underline{\sf{Solution-1}}[/tex]

Let assume that Cost price of good be Rs 100

Given that, gain % = 8

We know, Selling price, Cost price and gain % are connected by the relationship

[tex]\sf \: Selling \: price \: = \: \dfrac{(100 + Gain\%) \times Cost \: price}{100} \\ \\ [/tex]

So, on substituting the values, we get

[tex]\sf \: Selling \: price \: = \: \dfrac{(100 + 8) \times 100}{100} \\ \\ [/tex]

[tex]\sf\implies \sf \: Selling \: price \: = \: Rs \: 108 \\ \\ [/tex]

Now, we have

[tex] \sf \: Selling \: price \: = \: Rs \: 108 \\ \\ [/tex]

[tex]\sf \: Discount \: \% = 10 \\ \\ [/tex]

We know, Selling price, Marked price and Discount % are connected by the relationship

[tex]\sf \: Marked \: price \: = \: \dfrac{100 \times Selling \: price}{100 - Discount\%} \\ \\ [/tex]

So, on substituting the values, we get

[tex]\sf \: Marked \: price \: = \: \dfrac{100 \times 108}{100 - 10} \\ \\ [/tex]

[tex]\sf \: Marked \: price \: = \: \dfrac{100 \times 108}{90} \\ \\ [/tex]

[tex]\sf \: Marked \: price \: = \: \dfrac{10 \times 108}{9} \\ \\ [/tex]

[tex]\sf \: Marked \: price \: = \: 10 \times 12 \\ \\ [/tex]

[tex]\sf\implies \sf \: Marked \: price \: = \: Rs \: 120 \\ \\ [/tex]

So, we have

[tex]\sf \: Cost \: price \: = \: Rs \: 100 \\ \\ [/tex]

[tex]\sf \: Marked \: price \: = \: Rs \: 120 \\ \\ [/tex]

So,

[tex]\sf \: \% \: age \: above \: costprice = \dfrac{120 - 100}{100} \times 100 = 20 \\ \\ [/tex]

Hence,

[tex]\sf\implies \sf \: 20\% \: above \: the \:cost \: price \: should \: be \:marked \\ \\ [/tex]

[tex]\rule{190pt}{2pt}[/tex]

[tex]\large\underline{\sf{Solution-2}}[/tex]

Let assume that Marked price of an article be Rs 100.

So, given that there are two successive discounts of 20% and 5% on article.

So,

[tex]\sf \: Selling \: price = 100\bigg(1 - \dfrac{20}{100} \bigg) \bigg(1 - \dfrac{5}{100} \bigg) \\ \\ [/tex]

[tex]\sf \: Selling \: price = 100\bigg(1 - \dfrac{1}{5} \bigg) \bigg(1 - \dfrac{1}{20} \bigg) \\ \\ [/tex]

[tex]\sf \: Selling \: price = 100\bigg( \dfrac{5 - 1}{5} \bigg) \bigg(\dfrac{20 - 1}{20} \bigg) \\ \\ [/tex]

[tex]\sf \: Selling \: price = 100\bigg( \dfrac{4}{5} \bigg) \bigg(\dfrac{19}{20} \bigg) \\ \\ [/tex]

[tex]\sf\implies \sf \: Selling \: price = Rs \: 76 \\ \\ [/tex]

Now,

[tex]\sf \: Marked \: price \: = \: Rs \: 100 \\ \\ [/tex]

[tex]\sf \: Selling \: price \: = \: Rs \: 76 \\ \\ [/tex]

So,

[tex]\sf \: Discount\% = \dfrac{Marked \: price - Selling \: price}{Marked \: price} \times 100 \\ \\ [/tex]

[tex]\sf \: Discount\% = \dfrac{100 - 76}{100} \times 100 \\ \\ [/tex]

[tex]\sf\implies \sf \: Discount\% = 24 \\ \\ [/tex]