Cost and Management AccountingQuestion 5439 of 251
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1. At what quantity of purchase of batteries, the ordering costs will be equal to the inventory carrying costs?

Options

A1,600
B1,700
C1,800
D1,900
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Correct Answer

✅ Option A — 1,600

All Options:

  • A1,600 ✓
  • B1,700
  • C1,800
  • D1,900

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Detailed Solution & Explanation

In inventory management, the ordering cost and carrying cost are mathematically equal at the Economic Order Quantity (EOQ).
At EOQ: Total Ordering Cost=Total Carrying Cost\text{At EOQ: } \text{Total Ordering Cost} = \text{Total Carrying Cost}
Let the EOQ for batteries be calculated as:
EOQ=2×A×OC\text{EOQ} = \sqrt{\frac{2 \times A \times O}{C}}
Given:
- Annual demand (A\displaystyle A) = 54,000 batteries
- Ordering cost (O\displaystyle O) = ₹9,000 per order
- Carrying cost (C\displaystyle C) = 37.5%×₹800=₹300\displaystyle 37.5\% \times ₹800 = ₹300 per unit per annum
EOQ=2×54,000×9,000300=3,240,000=1,800 batteries\text{EOQ} = \sqrt{\frac{2 \times 54,000 \times 9,000}{300}} = \sqrt{3,240,000} = 1,800 \text{ batteries}
At this quantity (1,800\displaystyle 1,800 batteries), the ordering cost and carrying cost are equal.
Hence, **Option A** is the correct answer.

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