Question

A shopkeeper bought 200 articles costing the same if we sold 30% of the article at 20% loss and remaining at 10% profit if the total profit made by him is rupees 220 find the CP of an article​

Answer 1

Answer:

The CP of one article is Rs.110

Step-by-step explanation:

Total number of articles = 200

Let the CP of each article = "x"

Part 1

30% articles were sold at 20% loss

30% of 200 = 0.3*200 = 60

=> 60 articles were sold at 20% loss

CP of 60 articles = 60x

There was a loss of 20% in the transaction. This means:

SP = CP - (20% of CP)

SP = CP - 0.2*CP

SP = 0.8*CP

Now, CP = 60x

=> SP = 0.8*60x

=> SP = 48x

Part 2

70% articles were sold at 10% profit

70% of 200 = 0.7*200 = 140

=> 140 articles were sold at 10% profit

CP of 140 articles = 140x

There was a profit of 10% in the transaction. This means:

SP = CP + (10% of CP)

SP = CP + 0.1*CP

SP = 1.1*CP

Now, CP = 140x

=> SP = 1.1*140x

=> SP = 154x

For overall transaction of 200 articles

CP = 200x

SP = 48x + 154x

SP = 202x

Profit = SP - CP

          = 202x - 200x

          = 2x

ATQ, total profit = Rs.220

=> 2x = 220

=> x = 110

The cost per article is Rs.110

Verify:

Total number of articles = 200

CP for 1 article = Rs.110 => Total CP = Rs.22,000

30% of articles sold at 20% loss

=> 60 articles sold at Rs.88 each

=> SP for 60 articles = Rs.5280

70% of articles sold at 10% profit

=> 140 articles sold at Rs.121 each

=> SP for 140 articles = Rs.16940

Total SP = Rs.(5280 + 16940) = Rs.22,220

Total CP = Rs.22,000

Total Profit = Total SP - Total CP

                   = 22220 - 22000

                   = 220

Total profit = Rs.220 (as given, thus verified)