Question

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 ​

Answer 1

★ Solution :-

First, we should find the values of selling prices of both items.

Selling price of first item :-

$\sf \leadsto \dfrac{(100 - Loss\%)}{100} \times CP$

$\sf \leadsto \dfrac{(100 - 10)}{100} \times 450$

$\sf \leadsto \dfrac{90}{100} \times 450$

$\sf \leadsto \dfrac{90}{2} \times 9$

$\sf \leadsto \dfrac{90 \times 9}{2} = \dfrac{810}{2}$

$\sf \leadsto \cancel \dfrac{810}{2} = 405$

Selling price of second item :

Let the profit percent be x%

$\sf \leadsto \dfrac{(100 + Profit\%)}{100} \times CP$

$\sf \leadsto \dfrac{(100 + x)}{100} \times 450$

$\sf \leadsto \dfrac{(100 + x)}{2} \times 9$

$\sf \leadsto \dfrac{900 + 9x}{2}$

Now, we should find the total cost and selling prices.

Total cost price :

$\sf \leadsto 450 + 450$

$\sf \leadsto Rs.900$

Total selling price :

$\sf \leadsto 405 + \dfrac{900 + 9x}{2}$

$\sf \leadsto \dfrac{810 + 900 + 9x}{2}$

$\sf \leadsto \dfrac{1710 + 9x}{2}$

Now, we should find the profit percentage of second item.

$\sf \leadsto Total \: profit = \dfrac{SP - CP}{CP} \times 100$

$\sf \leadsto 20\% = \dfrac{\dfrac{1710 + 9x}{2} - 900}{900} \times 100$

$\sf \leadsto 20\% = \dfrac{\dfrac{1710 + 9x}{2} - 900}{9}$

$\sf \leadsto 20 \times 9 = \dfrac{1710 + 9x - 1800}{2}$

$\sf \leadsto 180 = \dfrac{ - 90 + 9x}{2}$

$\sf \leadsto 180 \times 2 = - 90 + 9x$

$\sf \leadsto 360 = - 90 + 9x$

$\sf \leadsto 360 + 90 = 9x$

$\sf \leadsto 450 = 9x$

$\sf \leadsto x = \dfrac{450}{9}$

$\sf \leadsto x = 50\%$

Now, we can find the selling price of second item.

Selling price of second item :-

$\sf \leadsto \dfrac{(100 + Profit\%)}{100} \times CP$

$\sf \leadsto \dfrac{(100 + 50)}{100} \times 450$

$\sf \leadsto \dfrac{150}{100} \times 450$

$\sf \leadsto \dfrac{3}{2} \times 450$

$\sf \leadsto \dfrac{3 \times 450}{2} = \dfrac{1350}{2}$

$\sf \leadsto \cancel \dfrac{1350}{2} = 675$

Therefore, the selling price of second item is ₹675.

Answer 2

Step-by-step explanation:

cp of 2 items=₹450 each

one sold at a loss of 10% which is equal to

$450 - \frac{10}{100 } \times 450 \\ = 450 - 45 = 405$

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 =

$900 + \frac{20}{100} \times 900 \\ = 900 + 180 \\ 1080$

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