Ravi and Prakesh are selling fruit for a college fundraiser. Customers can buy small boxes of apples and large boxes of apples. Ravi sold 4 small boxes of apples and 5 large boxes of apples for a total of ₹102. Prakesh sold 7 small boxes of apples and 9 large boxes of apples for a total of ₹182. The cost of two small box of apples is:

Given:

Ravi's sales: 4 × (cost of small box) + 5 × (cost of large box) = ₹102

Prakesh's sales: 7 × (cost of small box) + 9 × (cost of large box) = ₹182

Formula Used:

Solving a system of linear equations.

Calculation:

Let the cost of a small box of apples be ₹s and the cost of a large box of apples be ₹l.

From Ravi's sales: 4s + 5l = 102 (Equation 1)

From Prakesh's sales: 7s + 9l = 182 (Equation 2)

Multiply Equation 1 by 9 and Equation 2 by 5 to eliminate l:

⇒ (4s + 5l) × 9 = 102 × 9 ⇒ 36s + 45l = 918 (Equation 3)

⇒ (7s + 9l) × 5 = 182 × 5 ⇒ 35s + 45l = 910 (Equation 4)

Subtract Equation 4 from Equation 3:

⇒ (36s + 45l) - (35s + 45l) = 918 - 910

⇒ 36s - 35s + 45l - 45l = 8

⇒ s = 8

The cost of one small box of apples is ₹8.

The cost of two small boxes of apples = 2 × s = 2 × 8 = ₹16.

The cost of two small boxes of apples is ₹16.