Question

A person sold a goat at a gain of 15%. Had he bought it for 25% less and sold it for Rs.60 less, he would have made a profit of 32%. The cost price of the goat was
Rs 300

Rs. 180

Rs 240

Rs 375
​

Answer 1

$\sf\large\underline\green{Let:-}$

$\sf{\implies Cost\:_{(a\:goat)}=x}$

$\sf\large\underline\green{To\: Find:-}$

$\sf{\implies Cost\:_{(a\:goat)}=?}$

$\sf\large\underline\green{Solution:-}$

• To calculate the cost price of goat at first we have to find out the selling price of goat at gain of 15% then calculate the new cost price and new selling after that we have to find the cost price of goat with the help of given clue in the question:-]

$\sf\large\underline\green{Formula\: used:-}$

$\sf\small\underline\purple{Case-(i)}$

$\tt{\implies SP=\dfrac{100+G\%}{100}*CP}$

$\tt{\implies SP=\dfrac{100+15}{100}*x}$

$\tt{\implies SP=\dfrac{115}{100}*x}$

$\tt{\implies SP=\dfrac{23x}{20}}$

$\sf\small\underline\purple{Case-(ii)}$

• Now calculate New Cp and Sp here:-]

$\tt{\implies New\:_{(CP)}=\dfrac{100-L\%}{100}*Original\:_{(CP)}}$

$\tt{\implies New\:_{(CP)}=\dfrac{100-25}{100}*x}$

$\tt{\implies New\:_{(CP)}=\dfrac{75x}{100}}$

$\tt{\implies New\:_{(CP)}=\dfrac{3x}{4}}$

• Now calculate New Sp here:-}

$\tt{\implies New\:_{(SP)}=\dfrac{100+G\%}{100}*New\:_{(CP)}}$

$\tt{\implies New\:_{(SP)}=\dfrac{100+32}{100}*\dfrac{3x}{4}}$

$\tt{\implies New\:_{(SP)}=\dfrac{132}{100}*\dfrac{3x}{4}}$

$\tt{\implies New\:_{(SP)}=\dfrac{99x}{100}}$

$\sf\small\underline\purple{Case-(iii)}$

• Now calculate the cost price of goat:-}

$\sf{\implies Old\:_{(SP)}-60=New\:_{(SP)}}$

$\tt{\implies \dfrac{23x}{20}-60=\dfrac{99x}{100}}$

$\tt{\implies \dfrac{23x}{20}-\dfrac{99x}{100}=60}$

$\tt{\implies \dfrac{115x-99x}{100}=60}$

$\tt{\implies \dfrac{16x}{100}=60}$

$\tt{\implies 16x=6000}$

$\tt{\implies x=Rs.375}$

$\sf\large{Hence,}$

$\tt\purple{\implies The\:cost\: price\:of\:the\: goat=Rs.375}$