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Question #4
If the absolute difference between the selling price of the article when there is 15% loss and 15% gain in
selling a article is Rs 450, then what is the cost price of the article?
Y Rs 1,200
Rs 1,500
Rs 2.000
Rs 2 200​

Answer 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 :-

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

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

Substituting the given values.

$\longrightarrow \sf {S.P = \Bigg ( \dfrac{100-15}{100} \Bigg ) \times x }$

$\longrightarrow \sf {S.P = \Bigg ( \dfrac{85}{100} \Bigg ) \times x }$

$\longrightarrow \sf {S.P = \dfrac{85}{100} x }$

Let it be the equation (1).

★ Calculating SP when there is 15% gain :-

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

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

Substituting the given values.

$\longrightarrow \sf {S.P = \Bigg ( \dfrac{100+15}{100} \Bigg ) \times x }$

$\longrightarrow \sf {S.P = \Bigg ( \dfrac{115}{100} \Bigg ) \times x }$

$\longrightarrow \sf {S.P = \dfrac{115}{100} x }$

Let it be the equation (2).

★ According to the question,

$\longrightarrow$ Selling price when there is 15% gain ― Selling price when there is 15% loss = Rs. 450

$\longrightarrow \sf { \dfrac{115}{100}x - \dfrac{85}{100}x = Rs. \: 450 }$

$\longrightarrow \sf { \dfrac{115x - 85 x}{100} = Rs. \: 450 }$

$\longrightarrow \sf { \dfrac{30x}{100} = Rs. \: 450 }$

$\longrightarrow \sf { \dfrac{3x}{10} = Rs. \: 450 }$

$\longrightarrow \sf { 3x = Rs. \: (450 \times 10) }$

$\longrightarrow \sf { 3x = Rs. \: 4500 }$

$\longrightarrow \sf { x = Rs. \: \cancel{\dfrac{4500}{3} }}$

$\longrightarrow \sf { x = Rs. \: 1500 }$

$\longrightarrow\underline{\boxed{ \sf { C.P = Rs. \: 1500 }}} \; \bigstar$

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

_____________________

★ Some related formulae :

• Gain = S.P – C.P
• Loss = C.P – S.P

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• $\rm { Gain \: \% = \Bigg( \dfrac{Gain}{C.P} \times 100 \Bigg)\%}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• $\rm { Loss \: \% = \Bigg( \dfrac{Loss}{C.P} \times 100 \Bigg)\%}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• $\rm { S.P = \dfrac{100+Gain\%}{100} \times C.P}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• $\rm { C.P =\dfrac{100}{100+Gain\%} \times S.P}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• $\rm { S.P = \dfrac{100-loss\%}{100} \times C.P}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• $\rm { C.P =\dfrac{100}{100-loss\%} \times S.P}$