Concept
The concept of ratio of two numbers can be extended to three or more numbers.
Let us see the above example of ladoos. The proportion of ghee, rawa and sugar is 1 : 3 : 2. Here proportion of ghee and rawa is 1 : 3 and that of rawa and sugar is 3 : 2, This means the proportion of ghee, rawa and sugar is 1 : 3 : 2.
Let us take k bowls of ghee, 3k bowls of rawa and 2k bowls of sugar.
Hence for 12 bowls of rawa, how much quantity of ghee and sugar is required can be found as follows.
Now 3k = 12 \ k = 4 and 2k = 8.
\ 4 bowls of ghee and 8 bowls of sugar is required.
The same concept can be extended for proportion of 4 or more entities.
If a, b, c, d are in the ratio 2 : 3 : 7 : 4 then let us assume that the numbers are 2m, 3m, 7m, 4m.
From the given information, value of m can be determined.
For example if the sum of these four numbers is 48,
we find these numbers. 2m + 3m + 7m + 4m = 16 m = 48
\ m = 3 \ 2m = 6, 3m = 9, 7m = 21, 4m = 12
\ required numbers are 6, 9, 21, 12 .
Ex (1) The proportion of compounds of nitrogen, phosphorous and potassium in certain fertilizer is 18 : 18 : 10. Here compound of nitrogen is 18%, compound of phosphorous is 18% and that of potassium is 10%. Remaining part is of other substances. Find the weight of each of the above compounds in 20 kg of fertilizer.
Solution : Let the weight of nitrogen compound in 20 kg of fertilizer be x kg.