Question

A shopkeeper sold an article for ₹450 at a loss 10% at what price should he sell it soas to gain 10%
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Answer 1

Answer:

Rs.550

Step-by-step explanation:

GIVEN =

S.P. = Rs.450

LOSS =10%

Profit 10%

Sp. =???

we know that ---

c.p. = s.p. + loss

Here ,,,,

CP = 100/100- loss percent × sp

= 100 / 100-10 ×450

= 100 / 90 ×450

C.P.= Rs 500

so , the actual price or cost price is Rs.500 .

Now S.P. on 10 % profit

S.P. = c.p. + profit

Profit = 500×10 /100

=Rs 50

S.P. = 500 + 50

= Rs.550

So , they sell at Rs.550 to earn 10 % profit .

Answer 2

Answer:

The Selling price of the article to get a gain of 10% should be Rs. 550.

Step-by-step explanation:

Given :

Sold the article at = Rs. 450

Loss % = 10 %

To find :

Selling price to get 10% gain

Solution :

$\textsf{\underline{\underline{Case I -}}}$

Here :

• Selling Price = 450
• Loss % = 10 %
• Cost Price = ??

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

$\sf{\implies} \:{CP = \dfrac{100}{(100 - 10)} \times 450} \\ \\ \sf{\implies} \:{CP = \dfrac{100}{90} \times 450} \\ \\ \sf{\implies} \:{CP = \dfrac{10}{9} \times 450} \\ \\ \sf{\implies} \:{CP = \dfrac{4500}{9}} \\ \\ \sf{\implies} \:{CP =500}$

Cost Price of the article = Rs. 500

$\rule{300}{1.5}$

$\textsf{\underline{\underline{Case II - }}}$

Here :

• Cost Price = 500
• Gain % = 10 %
• Selling Price = ??

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

$\sf{\implies}\:{SP = \dfrac{(100 + 10)} {100} \times 500} \\ \\ \sf{\implies}\:{SP = \dfrac{110}{1} \times 5} \\ \\ \sf{\implies}\:{SP =550 }$

Selling Price = Rs. 550

$\therefore$ The Selling price of the article to get a gain of 10% should be Rs. 550.