Quantitative aptitude · lesson 23 of 30 · free

Mixtures and alligation — Quantitative aptitude for kids

When two kinds of rice, tea or juice are mixed, the mix price lies between the two. Alligation is a shortcut: the amounts are in the ratio of the differences, crossed over. For milk and water, remember the milk does not change when you add water.

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The method

Alligation cross — “cheaper : dearer = (dearer − mean) : (mean − cheaper)”

  1. Alligation: cheaper : dearer = (dearer price − mix price) : (mix price − cheaper price).
  2. Mix price = total cost ÷ total quantity.
  3. Adding water: the milk stays the same — use it to find the new water.
  4. Percent in a mix = amount of that thing ÷ total × 100.

Use it for: Mixing grades of rice or tea, milk and water, juice drinks, and mixture questions in aptitude tests.

Worked example: Rice at ₹40 per kg is mixed with rice at ₹60 per kg to make a mix worth ₹48 per kg. How many kg of the cheaper rice must be mixed with 20 kg of the dearer rice? → 30

  1. Cheaper : dearer = (60 − 48) : (48 − 40) = 12 : 8 = 3 : 2.
  2. Dearer = 20 kg = 2 parts, so 1 part = 10 kg. Cheaper = 3 × 10 = 30 kg.

Check: 30 × 40 + 20 × 60 = 1200 + 1200 = 2400, and 2400 ÷ 50 kg = ₹48 per kg ✓

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