Question

An article is sold for Rs 500 and hence a loss is incurred. Had the article been sold for Rs 700, the shopkeeper would have gained three times the former loss. What is the cost price of the article ?​

Answer 1

Answer:

Rupees 550

Step-by-step explanation:

Let the cost price be C and the loss occurred be L. If we go by the condition of the question, we'll get the following two equations:

C + 3L = 700 and C-L= 500;

If we solve the following two equations, We need to multiply the latter equation by 3 and then adding the 2 equations.

After adding the equations, we get

4C = 2200

C = 550

Here C was cost price, so this is the final answer, you can verify it from the question

Answer 2

Answer:

Rs 550

Step-by-step explanation:

Let us assume the cost price of the article is x.

CASE 1: When selling price is Rs 500

Selling price of article = Rs 500

Cost price of article = Rs x

Since loss has been incurred, Cost price > Selling price

Thus loss = Cost price - selling price = Rs (x - 500)

CASE 2: When selling price is Rs 700

Selling price of article = Rs 700

Cost price of article = Rs x

Since gain is incurred, Selling price > Cost price

Thus, gain = selling price - cost price = Rs ( 700- x)

According to question, Gain in case 2 = 3 x loss in case 1

Putting values that we have got,

700 - x = 3( x - 500 )

⇒ 700 - x = 3x - 1500

⇒ 3x + x = 700 + 1500

⇒ 4x = 2200

⇒ x = 550

Hence, cost price of the article is Rs 550.

CHECK:

Cost price = Rs 550

Selling price = Rs 500

Thus, loss = Rs 550 - 500 = Rs 50

When selling price = Rs 700

Gain = Rs 700 - 550 = Rs 150

We can see that Gain is 3 times of the loss incurred, which satisfies the given condition in the question.