Parcel Counter: Chargeable Weight and Slab Arithmetic
At a railway parcel office, the chargeable weight of a consignment is the greater of its actual weight and its volumetric weight, where volumetric weight in kilograms equals length × breadth × height in centimetres, divided by 5,000. Charges are: up to 5 kg - a flat ₹50; above 5 kg up to 20 kg - ₹50 plus ₹15 for every kg (or part kg) above 5; above 20 kg - ₹275 plus ₹12 for every kg (or part kg) above 20. A registered consignor who books regularly asks you to quote for three items: Item A, a carton measuring 40 cm × 30 cm × 25 cm, actual weight 4 kg; Item B, a carton measuring 50 cm × 40 cm × 30 cm, actual weight 18 kg; Item C, a crate of negligible volume, actual weight 24 kg. The consignor mentions that a competing agency divides by 6,000 instead of 5,000 and offers a flat 10 per cent discount, and asks whether he should switch.
1. Calculate the chargeable weight and the charge for Item A and Item B. Show the volumetric weight calculation for each.
Read the worked answer
Item A: volume = 40 × 30 × 25 = 30,000 cm³. Volumetric weight = 30,000 ÷ 5,000 = 6 kg. Actual weight is 4 kg, so chargeable weight = 6 kg. Charge: 6 kg falls in the 5–20 kg slab → ₹50 + ₹15 × (6 − 5) = ₹50 + ₹15 = ₹65.
Item B: volume = 50 × 40 × 30 = 60,000 cm³. Volumetric weight = 60,000 ÷ 5,000 = 12 kg. Actual weight is 18 kg, which is greater, so chargeable weight = 18 kg. Charge: ₹50 + ₹15 × (18 − 5) = ₹50 + ₹195 = ₹245.
The trap in Item A is to bill the 4 kg actual weight; the trap in Item B is to bill the 12 kg volumetric figure. In both cases the rule is 'greater of the two', not 'the figure you computed last'.
2. Is it cheaper for the consignor to book Item C as one 24 kg crate or as two 12 kg crates? Show both calculations and give a practical recommendation.
Read the worked answer
One 24 kg crate: above 20 kg, so charge = ₹275 + ₹12 × (24 − 20) = ₹275 + ₹48 = ₹323.
Two 12 kg crates: each falls in the 5–20 kg slab → ₹50 + ₹15 × (12 − 5) = ₹50 + ₹105 = ₹155 each. Total = 2 × ₹155 = ₹310.
Splitting saves ₹323 − ₹310 = ₹13, about 4 per cent.
The arithmetic answer is 'split', but the practical answer is more cautious: two consignments mean two receipts, two handling cycles and two chances of damage or misplacement for a 24 kg crate, and ₹13 is small against that risk. Recommend splitting only if the consignor already has two secure packages and the contents are not fragile; otherwise book as one. A good counter clerk quotes the cheaper figure but states the condition attached to it.
3. The consignor says the competitor divides by 6,000, which 'must be cheaper'. Test that claim on Item A and Item B, and say what you would advise him.
Read the worked answer
Item A under ÷6,000: 30,000 ÷ 6,000 = 5 kg volumetric, against 4 kg actual, so chargeable weight becomes 5 kg instead of 6 kg. Charge at your rates would be ₹50 (flat, since 5 kg is the slab limit) instead of ₹65 - a ₹15 difference.
Item B under ÷6,000: 60,000 ÷ 6,000 = 10 kg volumetric, but actual weight is 18 kg. Since the rule is 'greater of the two', the chargeable weight stays at 18 kg and the charge is unchanged at ₹245.
So the divisor only helps when the volumetric figure is the one being billed - bulky, light cartons like Item A. For dense cargo like Item B it changes nothing. The competitor's 10 per cent discount is a separate and larger factor and must be compared on the total bill, not on the divisor alone. Advise the consignor: get a written quote for all three items from both agencies and compare totals; the divisor is a headline, not a price.