Question

Sakshi sells coffee at a profit of 12% . If he reduces the price by ₹ 29 per kg, he would make a loss of 17%. Find the initial selling price per kg of coffee.

Answer 1

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

$\rm{\implies The\: initial\:CP\:_{(coffee)}=x}$

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

$\rm{\implies The\: initial\:CP\:_{(coffee)}=?}$

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

• To calculate initial price of per kg coffee we have calculate selling price of coffee when profit on 12% and loss on 17% separately here]

$\sf\small\underline{Calculate\:SP\: profit\:on\:12\%:}$

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

$\tt{\implies SP=\dfrac{100+12}{100}\times\:x}$

$\tt{\implies SP=\dfrac{112x}{100}}$

$\sf\small\underline{Calculate\:SP\:loss\:on\:17\%:}$

$\tt{\implies SP=\dfrac{100-L\%}{100}\times\:CP}$

$\tt{\implies SP=\dfrac{100-17}{100}\times\:x}$

$\tt{\implies SP=\dfrac{83x}{100}}$

• Note here as given in Question that he would make a loss of 17% when he reduces the price by Rs. 29 per kg. It means here Rs. 29 is the difference between initial selling and reducing selling price.]

$\tt{\implies SP\:_{(profit\:on\:12\%)}-SP\:_{(loss\:on\:17\%)}=29}$

$\tt{\implies \dfrac{112x}{100}-\dfrac{83x}{100}=29}$

$\tt{\implies \dfrac{112x-83x}{100}=29}$

$\tt{\implies \dfrac{29x}{100}=29}$

$\tt{\implies 29x=2900\implies x=100}$

$\sf\large{Hence,}$

$\rm{\implies The\: initial\:CP\:_{(coffee)}=Rs.100}$

Answer 2

$\mathcal{\huge{\underline{\underline{\red{Question\:?}}}}}$

✴Sakshi sells coffee at a profit of 12% . If he reduces the price by ₹ 29 per kg, he would make a loss of 17%. Find the initial selling price per kg of coffee.

$\mathcal{\huge{\fbox{\orange{AnSwEr:-}}}}$

✒ The initial selling price is Rs.100 per kg of coffee.

$\mathcal{\huge{\fbox{\fbox{\pink{Solution:-}}}}}$

Let, The initial SP be = x

➡ [Coffee selled at a profit of 12% . If he reduces the price by ₹ 29 per kg, he would make a loss of 17%.] {given}

✏ Calculating CP on 12 %

$\tt{\implies CP=\dfrac{100+G\%}{100}\times\:CP}$

$\tt{\implies CP=\dfrac{100+12}{100}\times\:x}$

$\tt{\implies CP=\dfrac{112x}{100}}$

✏ Calculating CP on 12 %

$\tt{\implies CP=\dfrac{100-L\%}{100}\times\:CP}$

$\tt{\implies CP=\dfrac{100-17}{100}\times\:x}$

$\tt{\implies CP=\dfrac{83x}{100}}$

According to the question,

➡ {CP on 12% - CP on 17%} = 29

$\tt{\implies \dfrac{112x-83x}{100}=29}$

$\tt{\implies \dfrac{29x}{100}=29}$

$\tt{\implies 29x=2900\implies x=100}$

Hence,

➡ The initial S.P. of coffee is Rs. 100 per kg.

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