Question

An article is sold for rs 500 and hence a loss is incurred. had the article been sold for rs 700 ,the shopkeeper would have gained three times the former loss. what is the cost price of the article solve the question properly please properly but answer is 550 but kase aya kyi bta do please ​

Answer 1

$\Large {\underline { \sf {Clarification :}}}$

Before commencing the steps, let's check out the procedure.

Here, we are given that the selling price of article is Rs. 500 and there is some loss. If article had been sold for rs 700, the shopkeeper would have gained three times the former loss.

We have to find out the cost price of the article.

At first, we'll assume the loss incurred by shopkeeper after selling the article at Rs. 500 as "x". After that, by using the formula of Gain and loss, we'll form suitable equations. By solving the equations, we'll find the cost price.

$\Large {\underline { \sf {Explication\: of \: steps :}}}$

Let us assume the former loss as "x".

First condition :

We know that,

★ Loss = CP - SP

Substitute the value of selling price and loss in the above formula.

→ x = CP - 500

• Transpose - 500 from RHS to LHS.

From this equation, we can say that :

→ $\boxed{\bf {x + 500 = CP}}$

Now, we have to find the value of "x" and substitute it in the above equation to find the cost price.

$\underline{\small \sf {\maltese \; \; \; According \: to \: the \: question : \; \; \; }}$

Second condition :

As per the given question, it is stated that if article had been sold for Rs. 700, the shopkeeper would have gained three times the former loss.

That means, in this condition selling price is Rs. 700.

We know that,

★ Gain = SP - CP

Substitute the value of selling price (in this condition) and CP from the first condition.

→ 3( Former loss ) = SP - CP

→ 3x = 700 - ( x + 500 )

→ 3x = 700 - x - 500

→ 3x + x = 700 - 500

→ 4x = 200

→ x = $\sf \dfrac{200}{4}$

→ x = 50

Therefore,

→ $\underline{ \boxed{\bf {Loss = Rs. \: 50 }}}$

• As we have assumed former loss as "x".

Now, again coming to the first condition.

According to the first condition, we have :

→ $\boxed{\bf {x + 500 = CP}}$

$\longrightarrow$ Rs. ( 50 + 500 )= CP

$\longrightarrow \underline{ \boxed{\bf {Rs. \: 550 = CP }}}$

Therefore, cost price of the article is Rs. 550.

Hence, we got the answer !

More formulae :

• Gain = S.P – C.P
• Loss = C.P – S.P

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

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

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

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

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

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