Akshay has 30 articles, each having the same cost price. He marked the price of each article at 30% above its cost price. He sold 15 of the articles at a discount of 20% each, and the remaining 15 articles at a discount of 10% each, thereby gaining a total profit of ₹630. What was the cost price of each article?

Let's assume the cost price of each article is 'y'.

Akshay has 30 articles, each having the same cost price.

Cost price of 30 articles = $$30\times y$$ = 30y    Eq.(i)

He marked the price of each article at 30% above its cost price.

marked price of each article = (100+30)% of y

= 130% of y

= 1.3y

marked price of 30 articles = $$30\times 1.3y$$ = 39y

marked price of 15 articles = $$\frac{39y}{2}$$ = 19.5y

He sold 15 of the articles at a discount of 20% each.

Selling price of 15 articles = 19.5y of (100-20)%

= 19.5y of 80%

= $$19.5y\times\frac{80}{100}$$

= 15.6y    Eq.(ii)

the remaining 15 articles at a discount of 10% each.

Selling price of remaining 15 articles = 19.5y of (100-10)%

= 19.5y of 90%

= $$19.5y\times\frac{90}{100}$$

= 17.55y    Eq.(iii)

Gaining a total profit of ₹630.

total profit = Eq.(ii)+Eq.(iii)-Eq.(i)

630 = 15.6y+17.55y-30y

630 = 33.15y-30y

630 = 3.15y

y = 200

Cost price of each article = ₹200