A candle factory has fixed costs of Rs 20,000. It sells candles at Rs 30 per dozen, and the variable cost is Rs 1.50 per candle. Based on these cost and price figures, what is the break even quantity of candles that the factory must sell to cover its costs?

Introduction / Context:
This question is about break even analysis in cost and management accounting. Break even analysis helps a firm determine the number of units it must sell so that total revenue exactly equals total cost, resulting in zero profit and zero loss. It is a key tool for pricing decisions, capacity planning, and understanding the viability of a business. Here, the factory produces candles and we are given fixed cost, selling price, and variable cost, from which we must compute the break even quantity of candles.

Given Data / Assumptions:

• Fixed cost of the factory: Rs 20,000.
• Selling price: Rs 30 per dozen candles.
• Variable cost: Rs 1.50 per candle.
• We assume that all candles produced are sold.
• We are asked for the break even quantity in terms of number of candles.

Concept / Approach:
Break even quantity is computed using the formula: break even quantity = fixed cost / contribution per unit. Contribution per unit is the selling price per unit minus the variable cost per unit. In this question, the data are partly given per dozen and partly per candle, so the first step is to convert everything into the same unit, either per candle or per dozen. Working per candle is convenient because the variable cost is already given per candle, so we convert the selling price per dozen into selling price per candle and then compute the contribution per candle.

Step-by-Step Solution:
Step 1: Compute the selling price per candle. Selling price per dozen = Rs 30, so selling price per candle = Rs 30 / 12 = Rs 2.50. Step 2: Note the variable cost per candle. Variable cost per candle = Rs 1.50. Step 3: Compute contribution per candle. Contribution per candle = Selling price per candle − Variable cost per candle = 2.50 − 1.50 = Rs 1.00. Step 4: Use the break even formula. Break even quantity in candles = Fixed cost / Contribution per candle = 20,000 / 1.00 = 20,000 candles. Step 5: Match this figure with the options given.

Verification / Alternative check:
We can also work in dozens. Variable cost per dozen = 12 * 1.50 = Rs 18. Contribution per dozen = Selling price per dozen − Variable cost per dozen = 30 − 18 = Rs 12 per dozen. Break even quantity in dozens = 20,000 / 12 ≈ 1,666.67 dozens. Multiplying back, 1,666.67 dozens times 12 candles per dozen gives 20,000 candles, which confirms the figure obtained earlier. This cross check shows that our calculation is internally consistent whether we work per candle or per dozen.

Why Other Options Are Wrong:
Option B (10,000) would be correct only if the contribution per candle were Rs 2, but it is only Rs 1, so it understates the break even level. Option C (15,000) and option D (12,000) similarly fail to satisfy the relationship fixed cost = contribution per unit * quantity. None of these quantities multiplied by the actual contribution per candle of Rs 1 produces the fixed cost of Rs 20,000. Only 20,000 candles give the correct coverage of fixed costs.

Common Pitfalls:
One common mistake is mixing units, for example subtracting the variable cost per candle directly from selling price per dozen without conversion, which leads to an incorrect contribution figure. Another pitfall is using total revenue divided by total cost instead of the proper formula based on contribution. Students may also forget that fixed costs are not affected by the level of output and so must be fully covered by contribution. Careful attention to units and formula avoids these errors.

Final Answer:
The factory must sell 20000 candles to break even and cover its fixed costs.