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Question #4
If the absolute difference between the selling price of the article when there is 15% loss and 1

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1. Answer:

   The cost price of the article is 1,500.

   Step-by-step explanation:

   Here, as per the provided information in the given question, we have :

   • Difference between the selling price of the article when there is 15% loss and 15% gain in selling a article is Rs 450.

   We are asked to calculate the cost price of the article.

   Let us assume the cost price of article as Rs. x.

   ⇒ Cost price = Rs. x

   ★ Calculating SP when there is 15% loss :-

   [tex] \longrightarrow \underline{ \boxed {\sf { S.P = \Bigg ( \dfrac{100-Loss \%}{100} \Bigg ) \times C.P}} }\\ [/tex]

   • C.P (Cost price) = x
   • Loss % = 15 %

   Substituting the given values.

   [tex] \longrightarrow \sf {S.P = \Bigg ( \dfrac{100-15}{100} \Bigg ) \times x }\\ [/tex]

   [tex] \longrightarrow \sf {S.P = \Bigg ( \dfrac{85}{100} \Bigg ) \times x }\\ [/tex]

   [tex] \longrightarrow \sf {S.P = \dfrac{85}{100} x }\\ [/tex]

   Let it be the equation (1).

   ★ Calculating SP when there is 15% gain :–

   [tex] \longrightarrow \underline{ \boxed {\sf { S.P = \Bigg ( \dfrac{100+ Gain \%}{100} \Bigg ) \times C.P}} }\\ [/tex]

   • C.P (Cost price) = x
   • Gain % = 15 %

   Substituting the given values.

   [tex] \longrightarrow \sf {S.P = \Bigg ( \dfrac{100+15}{100} \Bigg ) \times x }\\ [/tex]

   [tex] \longrightarrow \sf {S.P = \Bigg ( \dfrac{115}{100} \Bigg ) \times x }\\ [/tex]

   [tex] \longrightarrow \sf {S.P = \dfrac{115}{100} x }\\ [/tex]

   Let it be the equation (2).

   ★ According to the question,

   [tex] \longrightarrow [/tex] Selling price when there is 15% gain ― Selling price when there is 15% loss = Rs. 450

   [tex] \longrightarrow \sf { \dfrac{115}{100}x – \dfrac{85}{100}x = Rs. \: 450 }\\ [/tex]

   [tex] \longrightarrow \sf { \dfrac{115x – 85 x}{100} = Rs. \: 450 }\\ [/tex]

   [tex] \longrightarrow \sf { \dfrac{30x}{100} = Rs. \: 450 }\\ [/tex]

   [tex] \longrightarrow \sf { \dfrac{3x}{10} = Rs. \: 450 }\\ [/tex]

   [tex] \longrightarrow \sf { 3x = Rs. \: (450 \times 10) }\\ [/tex]

   [tex] \longrightarrow \sf { 3x = Rs. \: 4500 }\\ [/tex]

   [tex] \longrightarrow \sf { x = Rs. \: \cancel{\dfrac{4500}{3} }}\\ [/tex]

   [tex] \longrightarrow \sf { x = Rs. \: 1500 }\\ [/tex]

   [tex] \longrightarrow\underline{\boxed{ \sf { C.P = Rs. \: 1500 }}} \; \bigstar\\ [/tex]

   Therefore, cost price of the article is Rs. 1500.

   _____________________

   ★ Some related formulae :

   • Gain = S.P – C.P
   • Loss = C.P – S.P

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   • [tex] \rm { Gain \: \% = \Bigg( \dfrac{Gain}{C.P} \times 100 \Bigg)\%} [/tex]

   ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

   • [tex] \rm { Loss \: \% = \Bigg( \dfrac{Loss}{C.P} \times 100 \Bigg)\%} [/tex]

   ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

   • [tex] \rm { S.P = \dfrac{100+Gain\%}{100} \times C.P} [/tex]

   ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

   • [tex] \rm { C.P =\dfrac{100}{100+Gain\%} \times S.P} [/tex]

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   • [tex] \rm { S.P = \dfrac{100-loss\%}{100} \times C.P} [/tex]

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   • [tex] \rm { C.P =\dfrac{100}{100-loss\%} \times S.P} [/tex]

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