Question

Amit runs a grocery store in a busy neighbourhood market. He stocks two varieties of lentils.

• The premium quality sells at ₹ 280 per kg.
• The standard quality sells at ₹ 240 per kg.

Customers in his area are price-conscious, so Amit wants to create a mixture of the two varieties that appears high quality but is also affordable. He decides to sell the mixture at ₹ 265 per kg.

In what ratio should the ₹ 240/kg and ₹ 280/kg varieties be mixed to obtain the mixture costing ₹ 265 per kg?

Answer 1

Let x be the quantity of ₹ 240/kg variety and y be the quantity of ₹ 280/kg variety.

Amit sells the mixture at ₹ 265 per kg.

∴ 240x + 280y = 265(x + y)

⇒ 240x + 280y = 265x + 265y

⇒ 240x − 265x + 280y − 265y = 0

⇒ −25x + 15y = 0

⇒ 15y = 25x

⇒ `y/x = 25/15`

⇒ `y/x = 5/3`

⇒ y : x = 5 : 3.

Hence, the ratio of ₹ 280/kg to ₹ 240/kg varieties is 5 : 3.