Verified answer

Answer:

[tex]\qquad \:\boxed{\begin{aligned}& \qquad \:\sf \:(1). \: Marked \: price \: of \: ring\: = \: 1700 \qquad \: \\ \\& \qquad \:\sf \:(2). \: \% \: age \: above \: the \: cost \: price \: = \: 30 \: \% \end{aligned}} \qquad \: \\ \\ [/tex]

Step-by-step explanation:

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

Given that,

Cost price of a ring = 1190

Gain % = 20

We know,

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

[tex]\sf \: Selling \: price = \dfrac{(100 + 20) \times 1190}{100} \\ \\ [/tex]

[tex]\sf \: Selling \: price = \dfrac{120 \times 119}{10} \\ \\ [/tex]

[tex]\sf \: Selling \: price = 12 \times 119 \\ \\ [/tex]

[tex]\sf\implies \sf \: Selling \: price = 1428 \\ \\ [/tex]

Now,

[tex] \sf \: Selling \: price \: of \: ring = 1428 \\ \\ [/tex]

[tex]\sf \: Discount\% = 16 \\ \\ [/tex]

We know,

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

[tex]\sf \: Marked \: price \: = \: \dfrac{1428 \times 100}{100 - 16} \\ \\ [/tex]

[tex]\sf \: Marked \: price \: = \: \dfrac{1428 \times 100}{84} \\ \\ [/tex]

[tex]\sf \: Marked \: price \: = \: 17 \times 100 \\ \\ [/tex]

[tex]\sf\implies \sf \: Marked \: price \: = \: 1700 \\ \\ [/tex]

Hence,

[tex]\sf\implies \sf \: Marked \: price \: of \: ring\: = \: 1700 \\ \\ [/tex]

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

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

Let assume that

Cost price of an article be Rs 100

Gain % = 17

We know,

[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 + 17) \times 100}{100} \\ \\ [/tex]

[tex]\sf\implies \sf \: Selling \: price \: = \: 117 \\ \\ [/tex]

Now, we have

[tex]\sf \: Selling \: price \: of \: an \: article \: = \: Rs \: 117 \\ \\ [/tex]

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

We know,

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

On substituting the values, we get

[tex]\sf \: Marked \: price \: = \: \dfrac{117 \times 100}{100 - 10} \\ \\ [/tex]

[tex]\sf \: Marked \: price \: = \: \dfrac{117 \times 100}{90} \\ \\ [/tex]

[tex]\sf \: Marked \: price \: = \: \dfrac{117 \times 10}{9} \\ \\ [/tex]

[tex]\sf \: Marked \: price \: = \: 13 \times 10\\ \\ [/tex]

[tex]\sf\implies \sf \: Marked \: price \: = \: Rs \: 130\\ \\ [/tex]

So, we have now

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

and

[tex]\sf \: Marked \: price \: of \: an \: article \: = \: Rs \: 130 \\ \\ [/tex]

So,

[tex]\sf \: \% \: age \: above \: the \: cost \: price \: = \: \dfrac{130 - 100}{100} \times 100 \%\\ \\ [/tex]

[tex]\sf\implies \sf \: \% \: age \: above \: the \: cost \: price \: = \: 30 \: \% \\ \\ [/tex]

Answer:

(1) 1700 Marked price

(2) Marked price is 30% above the cost price

Step-by-step explanation:

According to the question first jeweller allows a discount of 16% but still he gains 20% .

I m using short trick.

Using fraction mathod, first make ratio of percentages.

[tex] \rightarrow \boxed{ 16 \% \: = \frac{4}{25} } \\ \sf means \: 4 \: unit \: discount \: on \: 25 \: units \\ \boxed{ 20\% = \frac{1}{5} } \\ \sf \: means \: 1 \: unit \: profit \: on \: 5 \: unit \: [/tex]

[tex] \rightarrow \sf \: \: \: \: \: \: \: \: \: \: \: \: cp \: \: \: \: \: \: sp \: \: \: \: \: mp \: \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 21 \: \: \: \: 25 \\ \: \: \: \: \: \: \: 5 \: \: \: \: \: \: \: \: \: \: 6 \: [/tex]

now we know that SP is constant, hence make sp equal

CP : SP : MP = 35 : 42 : 50

Given cost price, 35 units = 1190 ₹ , 1 unit = 34₹

MP = 50 unit = 50×34 = ₹ 1700 is marked price.

For question No. 2 , have a look on file attachment.