QUESTION:-
A shopkeeper bought two items at ₹ 450 each. He sold one at loss of 10%. At what price should he sell the other so as to gain 20% on the whole transaction?
TOPIC : PROFIT OR LOSS
SUBJECT: MATHS
THE ANSWER SHOULD NOT BE CONFUSING LIKE IN THE ATTACHMENT
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★ Solution :-
First, we should find the values of selling prices of both items.
Selling price of first item :-
[tex] \sf \leadsto \dfrac{(100 - Loss\%)}{100} \times CP[/tex]
[tex] \sf \leadsto \dfrac{(100 - 10)}{100} \times 450[/tex]
[tex] \sf \leadsto \dfrac{90}{100} \times 450[/tex]
[tex] \sf \leadsto \dfrac{90}{2} \times 9[/tex]
[tex] \sf \leadsto \dfrac{90 \times 9}{2} = \dfrac{810}{2} [/tex]
[tex] \sf \leadsto \cancel \dfrac{810}{2} = 405[/tex]
Selling price of second item :
Let the profit percent be x%
[tex] \sf \leadsto \dfrac{(100 + Profit\%)}{100} \times CP[/tex]
[tex] \sf \leadsto \dfrac{(100 + x)}{100} \times 450[/tex]
[tex] \sf \leadsto \dfrac{(100 + x)}{2} \times 9[/tex]
[tex] \sf \leadsto \dfrac{900 + 9x}{2}[/tex]
Now, we should find the total cost and selling prices.
Total cost price :
[tex] \sf \leadsto 450 + 450[/tex]
[tex] \sf \leadsto Rs.900[/tex]
Total selling price :
[tex] \sf \leadsto 405 + \dfrac{900 + 9x}{2}[/tex]
[tex] \sf \leadsto \dfrac{810 + 900 + 9x}{2}[/tex]
[tex] \sf \leadsto \dfrac{1710 + 9x}{2}[/tex]
Now, we should find the profit percentage of second item.
[tex] \sf \leadsto Total \: profit = \dfrac{SP - CP}{CP} \times 100[/tex]
[tex] \sf \leadsto 20\% = \dfrac{\dfrac{1710 + 9x}{2} - 900}{900} \times 100[/tex]
[tex] \sf \leadsto 20\% = \dfrac{\dfrac{1710 + 9x}{2} - 900}{9}[/tex]
[tex] \sf \leadsto 20 \times 9 = \dfrac{1710 + 9x - 1800}{2}[/tex]
[tex] \sf \leadsto 180 = \dfrac{ - 90 + 9x}{2}[/tex]
[tex] \sf \leadsto 180 \times 2 = - 90 + 9x[/tex]
[tex] \sf \leadsto 360 = - 90 + 9x[/tex]
[tex] \sf \leadsto 360 + 90 = 9x[/tex]
[tex] \sf \leadsto 450 = 9x[/tex]
[tex] \sf \leadsto x = \dfrac{450}{9} [/tex]
[tex] \sf \leadsto x = 50\%[/tex]
Now, we can find the selling price of second item.
Selling price of second item :-
[tex] \sf \leadsto \dfrac{(100 + Profit\%)}{100} \times CP[/tex]
[tex] \sf \leadsto \dfrac{(100 + 50)}{100} \times 450[/tex]
[tex] \sf \leadsto \dfrac{150}{100} \times 450[/tex]
[tex] \sf \leadsto \dfrac{3}{2} \times 450[/tex]
[tex] \sf \leadsto \dfrac{3 \times 450}{2} = \dfrac{1350}{2} [/tex]
[tex] \sf \leadsto \cancel \dfrac{1350}{2} = 675[/tex]
Therefore, the selling price of second item is ₹675.
Step-by-step explanation:
cp of 2 items=₹450 each
one sold at a loss of 10% which is equal to
[tex]450 - \frac{10}{100 } \times 450 \\ = 450 - 45 = 405[/tex]
so he sell 1 item at =₹405
so he want to gain 20% in whole transaction
total cp=450×2=₹900
to make 20% profit =
[tex]900 + \frac{20}{100} \times 900 \\ = 900 + 180 \\ 1080[/tex]
so he had to sell both the items In such a way so that he can earn ₹1080 to make 20% profit
he had sold one item at ₹405
so other item should be sold at =1080-405=₹675
to get a profit of 20 % in whole transaction
₹675 is your answer mark me brainliest