If one man adds 6 litres of water to 10 litres of milk and another man adds 4 litres of water to 8 litres of milk. Find the ratio of milk in the two mixtures.

Correct — A. 'Ratio of milk in the two mixtures' means the share of milk in each mixture, not the litres of milk.

First mixture: 6 L water + 10 L milk = 16 L, so milk share = 10/16 = 5/8

Second mixture: 4 L water + 8 L milk = 12 L, so milk share = 8/12 = 2/3

Compare the two fractions over 24:
(5/8) × 24 = 15 and (2/3) × 24 = 16
Ratio = 15 : 16 → option (a)

Why the others are wrong

• (b)
  16 : 15 — 16 : 15 is the right pair in the wrong order. The first mixture is 5/8 milk and the second 2/3, and 5/8 is the smaller share, so the smaller number must lead.
• (c)
  12 : 11 — 12 : 11 matches nothing in the data: the milk amounts are 10 : 8, the totals are 16 : 12, and the milk shares are 5/8 : 2/3. None of the three reduces to 12 : 11.
• (d)
  16 : 17 — 16 : 17 has no source for the 17. Scaled to twenty-fourths the two shares are exactly 15 and 16, and no reading of 6, 10, 4 and 8 produces a 17.

A mixture item turns on which quantity you are comparing — the amount of milk, or the proportion of milk.

The litres of milk here are 10 and 8, a ratio of 5 : 4, which is not among the options. The proportions are 10/16 and 8/12, and the options are built from those.

To compare two fractions as a ratio, write them over a common denominator and read off the numerators. Over 24, 5/8 and 2/3 become 15/24 and 16/24, so the ratio is 15 : 16.

Key facts

• Mixture 1 totals 16 L and 10/16 = 5/8 of it is milk.
• Mixture 2 totals 12 L and 8/12 = 2/3 of it is milk.
• Two fractions become a ratio once they share a denominator: 5/8 and 2/3 become 15/24 and 16/24.

Common traps

• Comparing 10 litres of milk with 8 litres and answering 5 : 4, an amount ratio the options do not offer
• Reversing the order and picking 16 : 15
• Comparing milk with water (10 : 6 and 8 : 4) instead of milk with the whole mixture

No directly related past PYQ was found.