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  1. 045A snack pack shrinks from 100 g to 90 g while its price stays at Rs 50. What is the effective price rise per gram?Pricing, costing and unit economicsWarm upCorporate FP&ACost accounting

    Try it first

    Pick the effective price rise.

    Show the worked solution

    About 11.1%. Before, Rs 50 buys 100 g, Rs 0.500 a gram. After, Rs 50 buys 90 g, Rs 0.556 a gram. The rise is 100 over 90 less one, which is 10 over 90, or 11.1%. In general a size cut of x at the same price is a price rise of x divided by (1 minus x), always a little more than the cut.

    Why is a 10% smaller pack more than a 10% price rise?

    Think of sharing the same Rs 50 bill among 10 friends instead of 11. Each pays more, and the increase is measured against the new, smaller headcount. Price per gram is price divided by grams, so cutting the grams by 10% divides the price by 0.9, which raises it by 1/0.9 less one, 11.1%. The percentage fall in grams is measured on 100; the percentage rise in price per gram is measured on what is left, 90.

    A 10% smaller pack at the same price is an 11.1% price riseRs 0.500100 g for Rs 50Rs 0.55690 g for Rs 50per gram: up 11.1%, not 10%0%10%20%30%0%15%30%45%Pack size cutEffective price riseif rise = cut10% cut: 11.1%20%: 25%25%: 33.3%
    Rs 50 for 100 g is Rs 0.500 a gram and Rs 50 for 90 g is Rs 0.556 a gram, an 11.1% rise, and the gap between the cut and the rise grows with the cut: 20% smaller is 25% dearer and 25% smaller is 33.3% dearer.
    The relationship
    Price rise=11−x−1=x1−x=0.100.90=11.1%\text{Price rise} = \frac{1}{1-x} - 1 = \frac{x}{1-x} = \frac{0.10}{0.90} = 11.1\%
    xthe cut in pack size, as a decimal
    What it says in wordsA size cut of x at a fixed price is a price rise of x over one minus x.

    How would a finance team use this?

    Inflation in raw materials pushes consumer companies to protect a price point that shoppers remember, such as Rs 10 or Rs 50, and adjust grams instead. To compare price changes across products, convert every pack-size change into a price per unit, or a volume decline will be misread as stable pricing. In a revenue bridge, the same rupee sales on fewer grams show up as a price gain, not as flat sales. Say the limitation: price per gram is the right comparison only if quality and the mix of the pack stay the same.

    Where candidates lose it

    The trap answer is 10%, the size cut itself. It measures the change against the old pack, while the price per gram has to be measured against the new one.

    A second wrong answer is 9.1%, which comes from dividing 10 by 110. That is the rule for the opposite case, a pack that grows 10% at the same price, which is a 9.1% price cut.

    What the interviewer asks next

    • A pack grows from 100 g to 120 g at the same price. What is the price change per gram?
    • The pack shrinks to 90 g and the price falls to Rs 48. What is the net price change per gram?
    • How would you show this in a price-volume bridge?