Lessons · Pharmacy · alligation: mixing a strong and a weak
Alligation: mixing a strong one and a weak one
To reach a strength in between two you have, the parts of each are the differences taken across the diagonal.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
What it is for
The shelf holds a 30% and a 5% and the order wants a 12%. Nobody is going to deliver a 12%; it gets made, and alligation is how the two amounts are worked out in about twenty seconds.
How to think about it
Write the wanted strength in the middle, the strong one above and the weak one below. The parts of the STRONG one are the wanted less the weak. The parts of the WEAK one are the strong less the wanted. Add the parts, divide the batch by the total, and multiply each part share out. Then check: the wanted strength has to sit between the two, or no mixture of them can reach it.
Worked example
Want 10%, from a 25% and a 5%The wanted strength sits between the two, so it can be made.
Parts of the 25% = 10 - 5 = 5 partsThe wanted less the weaker, taken across the diagonal.
Parts of the 5% = 25 - 10 = 15 partsThe stronger less the wanted.
Total = 5 + 15 = 20 partsThen the batch is shared out in that ratio.
600 g / 20 = 30 g per part: 5 x 30 = 150 g of the 25%, 15 x 30 = 450 g of the 5%And 150 + 450 = 600 g, which is the check.
Your turn
You want a 20%, mixing a 50% and a 10%. Write the parts of the 50%.
20 - 10 = parts
Solve one, graded on the server
The trap
Crossing the wrong way and giving the strong one the big share. The closer the wanted strength sits to one of the two, the MORE of that one goes in; if your answer says otherwise, the diagonals were swapped.