Question

Article A was sold at a profit of 50% and Article B was sold at a loss of 10%, which resulted to a profit of Rs. 65 for both. If the selling price of Article A was 250% of that of Article B, what was the cost of Article A?

Answer 1

Cost price of article A = Rs. 141.3

Let cost price of article A be x and the cost price of article B be y.

Profit on A = 50%

Selling price of A = x + 50/100 × x

= 1.5 x

Loss on B = 10%

Selling price of B = y - 10/100 × y

= 0.9 y

For both A and B -

Profit = Rs. 65 = profit on A - loss on B

=> 65 = 0.5x - 0.1y -------(1)

Selling price of A is 250% of that of B.

(x / y) × 100 = 250

=> x = 2.5 y

Substituting the value of x in (1)

=> 65 = 0.5(2.5y) - 0.1y [x = 2.5 y]

=> 65 = 1.25y - 0.1 y

=> 1.15 y = 65

=> y = 56.52

x = 141.3

Cost price of article A = Rs. 141.3

Answer 2

Let CP of B is 100₹

Then SP of B is 90₹

According to the question SP of A is 250% of SP of B

So SP of A is 250% of 90= 225₹

Then CP of A becomes 225×100/150= 150₹

Profit obtained from selling Article A is 225₹-150₹=75₹

Loss obtained from selling Article B is 100₹-90₹=10₹

So overall transaction he gets 75₹-10₹=65₹

And according to the question also total profit obtained is 65₹.

So CP of Article A was also our assumption value 150₹