Verified answer

Answer:

[tex]\qquad\qquad\boxed{ \sf{ \:\sf\bf \:Gain \: \% = 15 \: \% \: }}\\ \\ [/tex]

Step-by-step explanation:

Given that,

[tex]\qquad\sf \:Cost \: of \: coffee \: per \: kg \: = \: \$ \: 250 \\ \\ [/tex]

[tex]\qquad\sf \:Cost \: of \: chicory \: per \: kg \: = \: \$ \: 75 \\ \\ [/tex]

Now, it is given that, Coffee contains $ 250 per kg was mixed with chicory costing $ 75 per kg in the ratio 5:2.

So,

[tex]\qquad\sf \:Amount \: of \: coffee \: per \: kg \: = \: \dfrac{5}{7} \\ \\ [/tex]

[tex]\qquad\sf \:Amount \: of \: chicory \: per \: kg \: = \: \dfrac{2}{7} \\ \\ [/tex]

Thus,

[tex]\qquad\sf \:Cost \: of \: \dfrac{5}{7} \: kg \: of \: coffee \: = \:\dfrac{5}{7} \times 250 = \$ \: \dfrac{1250}{7} \\ \\ [/tex]

and

[tex]\qquad\sf \:Cost \: of \: \dfrac{2}{7} \: kg \: of \: chicory \: = \:\dfrac{2}{7} \times 75 = \$ \: \dfrac{150}{7} \\ \\ [/tex]

So,

[tex]\qquad\sf \:Cost \: of \: 1 \: kg \: of \: mixture \: = \:\dfrac{1250}{7} + \dfrac{150}{7} = \dfrac{1400}{7} =\$ \: 200 \\ \\ [/tex]

Further given that,

[tex]\qquad\sf \:Selling \: Profit \: of \: 1 \: kg \: of \: mixture \: =\$ \: 230 \\ \\ [/tex]

[tex]\qquad\sf\implies Selling \: Price \: > \: Cost \: Price \\ \\ [/tex]

[tex]\qquad\sf\implies Gain \: in \: this \: transaction \\ \\ [/tex]

So,

[tex]\qquad\sf \:Gain \: \% = \dfrac{Selling \: Price - Cost \: Price}{Cost \: Price} \times 100\% \\ \\ [/tex]

On substituting the values, we get

[tex]\qquad\sf \:Gain \: \% = \dfrac{230 - 200}{200} \times 100\% \\ \\ [/tex]

[tex]\qquad\sf \:Gain \: \% = \dfrac{30}{2} \% \\ \\ [/tex]

[tex]\qquad\sf\bf\implies \:Gain \: \% = 15 \: \% \\ \\ [/tex]

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Additional Information

[tex]\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{{More \: Formulae}}}} \\ \\ \bigstar \: \bf{Gain = \sf S.P. \: – \: C.P.} \\ \\ \bigstar \:\bf{Loss = \sf C.P. \: – \: S.P.} \\ \\ \bigstar \: \bf{Gain \: \% = \sf \Bigg( \dfrac{Gain}{C.P.} \times 100 \Bigg)\%} \\ \\ \bigstar \: \bf{Loss \: \% = \sf \Bigg( \dfrac{Loss}{C.P.} \times 100 \Bigg )\%} \\ \\ \\ \bigstar \: \bf{S.P. = \sf\dfrac{(100+Gain\%) or(100-Loss\%)}{100} \times C.P.} \\ \: \end{array} }}\end{gathered}\end{gathered}\end{gathered}[/tex]