Question

by selling an article for Rs 195 a dealer make a profit of 30% by how much should be decrease is selling price so as to make a lost 10%​

Answer 1

Answer :-

◾We are provided with :-

▪️Selling Price of Article = Rs 195

▪️Profit gained by Seller on selling on SP = 30%

◾Now to reduce the cost in order to make the effective loss 10% .

⏩ Let the cost of article be "x"

◾Then we can say that

▪️x + 30% of x = 195

$\implies\sf{ x + \dfrac{30x}{100} = 195 }$

$\implies\sf{ \dfrac{100x + 30x}{100} = 195 }$

$\implies \sf{ \dfrac{130x}{100} = 195}$

$\implies \sf{ 130x = (195)(100) }$

$\implies \sf{\dfrac{ 195 \times 10\cancel{0}}{13\cancel{0}}}$

$\implies \sf{x = 15 \times 10}$

$\implies \sf{ x = 150}$

◾Now to make a loss of 10% the price

$\sf{ 150 - 10\% \:of\:150}$

$= \sf{ 150 - 15}$

$= \sf{ 135}$

◾Now the amount of cost which should be reduced

$\bf{ = 195 - 135}$

$\bf{ = 60}$

Answer 2

$\textbf{\underline{\underline{Answer :-}}}$

The shopkeeper needs to reduce Rs.60 from the Original Selling Price to get a Loss of 10%.

$\textbf{\underline{\underline{Explanation :-}}}$

$\textsf{\underline{\underline{Given :}}}$

Selling the article at = Rs.195 makes profit of 30%

$\textsf{\underline{\underline{To find :}}}$

The decrease in Selling price to make the loss 10%

$\textsf{\underline{\underline{Solution :}}}$

$\textbf{Case I}$

▪ Selling Price = Rs.195

▪ Profit % = 30%

▪ Cost Price = ?

$\star$ We know that :

${\boxed{\sf\:{CP = \frac{100}{(100 + profit\%)} \times SP}}}$

${\sf{\implies{CP = \dfrac{100}{(100 + 30\%)} \times195}}}$

$\sf{\implies} \: CP = \dfrac{100}{130} \times 195$

$\sf{\implies} \: CP = \dfrac{19500}{130}$

$\sf{\implies}\red{ \: CP = 150}$

$\textbf{Case II}$

▪ Cost Price = Rs.150

▪ Loss % = 10%

▪ Selling Price = ?

$\star$ We know that :

${\boxed{\sf\:{SP = \frac{(100-Loss\%)} {100} \times CP}}}$

$\sf{\implies} \: SP = \dfrac{100 - 10}{100} \times 150$

$\sf{\implies} \: SP = \dfrac{90}{100} \times 150$

$\sf{\implies} \: SP = \dfrac{13500}{100}$

$\sf{\implies}\red{ \: SP = 135}$

$\therefore$ The Selling price should be Rs.135 to get 10% loss.

Case I Selling Price = Rs.195

Case II Selling Price = Rs. 135

We need to subtract the Selling prices.

$\sf{\implies} \: 195 - 135$

$\sf{\implies}\red{\:60}$

$\therefore$ The shopkeeper needs to reduce Rs.60 from the Original Selling Price to get a Loss of 10%.