Apalpali cap is marked to sell at a profit of 10% by a shopkeeper. if he sells it at a discount of rs 10.50 there will be a loss of 5%.find the cost price of the cap

The cost price of the cap is Rs 70

Step-by-step explanation:

* Lets explain how to solve the problem

- A Palpali cap is marked to sell at a profit of 10% by a shopkeeper

- Let the cost price of the cap is x

∵ It marked to sell at a profit 10%

∴ Its selling price = x + (10/100) x = x + 0.1 x = 1.1 x ⇒ (1)

- He sells it at a discount 10.50

∴ He sells it at ⇒ 1.1 x - 10.50

- There will be loss of 5%

∵ selling price = cost price - loss

∵ The cost price is x

∴ selling price = x - (5/100) x = x - 0.05 x = 0.95 x ⇒ (2)

- Equate (1) and (2) ⇒ both of them is the selling price

∴ 1.1 x - 10.50 = 0.95 x

- Subtract 0.95 x  from both sides and add 10.50 to them

∴ 1.1 x - 0.95 x = 10.50

∴ 0.15 x = 10.50 ⇒ divide both sides by 0.15

∴ x = 70

∵ x is the cost price of the cap

∴ The cost price of the cap is Rs 70