x articles are bought at ₹ (x - 8) each and (x - 2) some other articles are bought at ₹ (x - 3) each. If the total cost of all these articles is ₹ 76, how many articles of first kind were bought ?

Since,

x articles are bought at ₹ (x - 8) each and (x - 2) some other articles are bought at ₹ (x - 3) each.

Total cost = x(x - 8) + (x - 2)(x - 3).

Given,

Total cost = ₹ 76.

∴ x(x - 8) + (x - 2)(x - 3) = 76

⇒ x² - 8x + x² - 3x - 2x + 6 = 76

⇒ 2x² - 13x + 6 - 76 = 0

⇒ 2x² - 13x - 70 = 0

⇒ 2x² - 20x + 7x - 70 = 0

⇒ 2x(x - 10) + 7(x - 10) = 0

⇒ (2x + 7)(x - 10) = 0

⇒ 2x + 7 = 0 or x - 10 = 0

⇒ 2x = -7 or x = 10

⇒ x = -$\dfrac{7}{2}$ or x = 10.

Since, no. of articles cannot be negative.

∴ x = 10.

Hence, there are 10 articles of first kind.