Ratios with more than two terms

Nothing says a ratio must have only two terms. Viswanath's spice mix grinds together 8 spoons of coriander seeds, 4 red chillies, 2 spoons of toor dal and 1 spoon of fenugreek.

That's the ratio 8 : 4 : 2 : 1: four terms, and the same rule applies. Every quantity must change by the same factor for the taste to stay the same.

Puneet wants the same mix but has only 2 red chillies. Viswanath used 4, so Puneet has half. Everything else must halve too.

So Puneet uses 4 spoons of coriander, 2 chillies, 1 spoon of toor dal and half a spoon of fenugreek: the ratio 4 : 2 : 1 : 0.5. We write 8 : 4 : 2 : 1 :: 4 : 2 : 1 : 0.5. (Multiplying or dividing every term by the same number like this is called scaling a ratio.)

In general, if a : b : c : d :: p : q : r : s, then a/p = b/q = c/r = d/s: one single factor running through every term.

A purple paint takes Red : Blue : White :: 2 : 3 : 5. Yasmin has 10 litres of white. White is 5 parts, so 5 parts is 10 litres and 1 part is 2 litres. Red is 2 parts = 4 litres; blue is 3 parts = 6 litres. Total: 4 + 6 + 10 = 20 litres.

Concrete works the same way, and matters more. It mixes cement, sand and gravel, and the ratio depends on the strength needed: 1 : 1.5 : 3 for pillars, beams and roofs (which are also strengthened with steel rods).

With 3 bags of cement, multiply every term by 3: cement : sand : gravel = 3 : 4.5 : 9. That's 3 + 4.5 + 9 = 16.5 bags of concrete altogether.