Question

Rohit sold an article to Kartik at a profit of 2.5% and Kartik sold this article to Manish at a loss of 10% . Manish paid ₹9.90 to Kartik. Find the cost price of the article for Rohit​

Answer 1

Answer:

• Cost price of the article for Rohit is ₹10.73.

Step-by-step explanation:

Given that:

• Rohit sold a article to Kartik at a profit of 2.5%.
• Kartik sold that article to Manish at a loss of 10%.
• Manish paid ₹9.90 to Kartik.

To Find:

• Cost price of the article for Rohit.

Let us assume:

• The cost price of the article for Rohit be x.

Calculating SP for Rohit:

As we know that,

$\sf{SP=\dfrac{(100+gain\%)}{100}\times CP}$

Substituting the values,

$\rm{SP=\dfrac{(100+2.5)}{100}\times x}$

Solving the bracket,

$\rm{=\dfrac{102.5}{100}\times x}$

Multiplying,

$\rm{=\dfrac{102.5x}{100}}$

Hence, SP for Rohit = 102.5x/100

Now,

• CP for Kartik = 102.5x/100

Calculating SP for Kartik:

As we know that,

$\sf{SP=\dfrac{(100-loss\%)}{100}\times CP}$

Substituting the values,

$\rm{SP=\dfrac{(100-10)}{100}\times \dfrac{102.5x}{100}}$

Solving the bracket,

$\rm{=\dfrac{90}{100}\times \dfrac{102.5x}{100}}$

Cutting off The zeros,

$\rm{=\dfrac{9\!\!\!\not{0}}{10\!\!\!\not{0}}\times \dfrac{102.5x}{100}}$

$\rm{=\dfrac{9}{10}\times \dfrac{102.5x}{100}}$

Multiplying,

$\rm{=\dfrac{922.5x}{1000}}$

According tot he question:

$\rm{\implies\dfrac{922.5x}{1000}=9.90}$

Transposing 1000 from LHS to RHS and changing its sign,

$\rm{\implies922.5x=9.90\times1000}$

Multiplying RHS,

$\rm{\implies922.5x=9900}$

Transposing 922.5 from LHS to RHS and changing its sign,

$\rm{\implies x=\dfrac{9900}{922.5}}$

Dividing RHS,

$\bf{\implies x=10.73}$

Hence,

• x = 10.73

Therefore,

• Cost price of the article for Rohit = x = ₹10.73