Multiple choice

Two samples of alloys containing silver and aluminium are marked as A and B. Sample A contains silver and aluminium in a ratio of 4 : 5 and sample B contains silver and aluminium in the ratio 5 : 1. We have to make another alloy using the alloys A and B, so that the ratio of silver to that of aluminium in the new alloy would be 5 : 4. Find the ratio of the alloy A to that of the alloy B, so that when mixed together, they achieve our aim.

  1. 5 : 3

  2. 5 : 1

  3. 1 : 2

  4. 5 : 2

  5. 2 : 5
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Use alligation on silver content. A: 4/9, B: 5/6, Mix: 5/9. (5/6 - 5/9) / (5/9 - 4/9) = (15/18 - 10/18) / (1/9) = (5/18) / (2/18) = 5/2.

AI explanation

Using the rule of alligation on the silver fractions, we calculate the silver fraction in alloy A as 4 divided by 9 and in alloy B as 5 divided by 6. The target silver fraction in the new alloy is 5 divided by 9. Applying the alligation method gives the ratio of alloy A to alloy B as (5 divided by 6 minus 5 divided by 9) to (5 divided by 9 minus 4 divided by 9). This simplifies to 5 divided by 18 to 1 divided by 9, which is equivalent to 5 to 2. The required ratio of alloy A to alloy B is 5 to 2.

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