shopkeeper marked the price of an article 40% above cp and sold it after giving 2 successive discounts of 10% and 15%.if profit is equal to rs 82.50,then what should be sp of article to a 20% profit on it?
To find the selling price (SP) that will yield a 20% profit, we can follow these steps:
Step 1: Calculate the cost price (CP) of the article.
Given that the shopkeeper initially marked the price of the article 40% above the cost price (CP), we can calculate the CP as follows:
Let x be the CP.
The marked price (MP) of the article is 40% above the CP:
MP = CP + 40% of CP
MP = CP + 0.4 * CP
MP = 1.4 * CP
Step 2: Calculate the selling price (SP) after giving 2 successive discounts.
The first discount is 10%, and the second discount is 15%.
To calculate the SP, we apply the discounts successively:
SP = MP - 10% of MP
SP = 0.9 * MP
Now, applying the second discount:
SP = 0.9 * MP - 15% of (0.9 * MP)
SP = 0.9 * MP - 0.15 * 0.9 * MP
SP = 0.9 * MP - 0.135 * MP
SP = 0.765 * MP
Given that the profit is equal to Rs 82.50, we have:
Profit = SP - CP
82.50 = 0.765 * MP - CP
Step 3: Calculate the selling price (SP) that will yield a 20% profit.
We need to find the SP that gives a 20% profit, so the profit would be 20% of the CP.
Let's calculate the new MP that will give the desired profit:
Profit = 20% of CP
Profit = 0.2 * CP
Now, we can calculate the new MP:
MP = CP + Profit
MP = CP + 0.2 * CP
MP = 1.2 * CP
Given that the profit is equal to Rs 82.50, we have:
82.50 = 0.765 * MP - CP
Solving these two equations will give us the value of CP and MP, which we can then substitute back to find the final SP.
Please provide the values for the profit and any additional information to continue with the calculations.