They are at a shop to buy badam drink mix. They are looking at two products and wondering which has a larger share of badam. Can you figure it out? Which product uses a smaller proportion of food chemicals? [DEF: sugar 99 g, milk solids 30 g, badam powder 12 g, food chemicals 9 g, total weight 150 g. Zacni: sugar 272 g, milk solids 64 g, badam powder 40 g, food chemicals 24 g, total weight 400 g.]
Answer
Zacni has the larger share of badam. Neither uses a smaller proportion of food chemicals — the two are equal.
Badam in DEF = 12/150 × 100 = 8%
Badam in Zacni = 40/400 × 100 = 10%
Food chemicals in DEF = 9/150 × 100 = 6%
Food chemicals in Zacni = 24/400 × 100 = 6%
Why it happens: Reading the raw grams misleads you twice over. Zacni lists 40 g of badam against DEF's 12 g — more than three times as much — but the packet is also much larger, so the share rises only from 8% to 10%. And Zacni's 24 g of food chemicals looks far worse than DEF's 9 g, yet as a proportion of what you actually drink the two are identical at 6%. Comparing packets of different sizes is exactly the situation percentages were invented for.
Q2.
Complete this table by calculating the percentages to answer the questions: [rows DEF and Zacni; columns Sugar, Milk Solids, Badam Powder, Food Chemicals; DEF's sugar entry 66% is given.]
Did you know? In both packets sugar is the largest ingredient by a long way — two-thirds of the contents. Madhu's joke, that it should be called a “sugar drink mix”, is arithmetically fair.
Q3.
Check if the percentages of each product add up to 100.
The weights agree as well: 99 + 30 + 12 + 9 = 150 g, and 272 + 64 + 40 + 24 = 400 g.
Why it happens: Each percentage is one ingredient divided by the total weight. Adding them adds the numerators over a common denominator, and the ingredients add back to the total weight — so the sum must be total/total = 1 = 100%. If a label's percentages did not add to 100, either an ingredient has been left off the list or one of the figures is wrong. That makes this a genuinely useful check on any packet you pick up.