Question

Two products, P and Q, are sold in the ratio of 10:1. The fixed cost is Rs. 1,40,000. The selling price of P is Rs. 10/unit and Q is Rs. 40/unit. The variable costs of P and Q are Rs. 5/unit and Rs. 20/unit, respectively. The break-even point in terms of revenue, in Rs., is ................. (in integer).

Hint:

The break-even point in terms of revenue can be found by equating total revenue to total cost, considering both fixed and variable costs.

Answer 1

Let the number of units of P and Q sold be \( x \) and \( y \), respectively. Since the products are sold in the ratio 10:1, we have the relationship: \[ \frac{x}{y} = 10 → x = 10y \] Let \( y \) be the number of units of Q sold.
- The revenue from selling \( x \) units of P and \( y \) units of Q is: \[ R = 10x + 40y = 10(10y) + 40y = 140y \] - The total variable cost for selling \( x \) units of P and \( y \) units of Q is: \[ VC = 5x + 20y = 5(10y) + 20y = 70y \] - The total cost (fixed + variable) is: \[ C = 1,40,000 + 70y \] At the break-even point, revenue equals cost: \[ R = C \] \[ 140y = 1,40,000 + 70y \] \[ 70y = 1,40,000 → y = \frac{1,40,000}{70} = 2000 \] Thus, \( x = 10y = 20,000 \). The total revenue is: \[ R = 140y = 140 \times 2000 = 2,80,000 \]