Ratio, Proportion, Indices, LogarithmMTP Jun 23 - Series IIQuestion 859 of 220
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Two vessels containing water and milk in the ratio 2:3\displaystyle 2:3 and 4:5\displaystyle 4:5 are mixed in the ratio 1:2\displaystyle 1:2. The ratio of milk and water in the resulting mixture.

Options

A58:77\displaystyle 58:77
B77:58\displaystyle 77:58
C68:77\displaystyle 68:77
DNone of these
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Correct Answer

✅ Option b — 77:58\displaystyle 77:58

All Options:

  • A58:77\displaystyle 58:77
  • B77:58\displaystyle 77:58
  • C68:77\displaystyle 68:77
  • DNone of these

Detailed Solution & Explanation

Let us calculate the total quantity of water and milk in the resulting mixture from the two vessels mixed in the ratio 1:2\displaystyle 1:2.
Assume we take 1\displaystyle 1 unit volume of Vessel 1 and 2\displaystyle 2 unit volumes of Vessel 2.

**Vessel 1 (Water : Milk = 2:3\displaystyle 2:3):**
- Total parts = 2+3=5\displaystyle 2 + 3 = 5
- Fraction of Water = 25\displaystyle \frac{2}{5}
- Fraction of Milk = 35\displaystyle \frac{3}{5}
Since we take 1\displaystyle 1 unit from Vessel 1:
- Water contribution = 1×25=25\displaystyle 1 \times \frac{2}{5} = \frac{2}{5} units
- Milk contribution = 1×35=35\displaystyle 1 \times \frac{3}{5} = \frac{3}{5} units

**Vessel 2 (Water : Milk = 4:5\displaystyle 4:5):**
- Total parts = 4+5=9\displaystyle 4 + 5 = 9
- Fraction of Water = 49\displaystyle \frac{4}{9}
- Fraction of Milk = 59\displaystyle \frac{5}{9}
Since we take 2\displaystyle 2 units from Vessel 2:
- Water contribution = 2×49=89\displaystyle 2 \times \frac{4}{9} = \frac{8}{9} units
- Milk contribution = 2×59=109\displaystyle 2 \times \frac{5}{9} = \frac{10}{9} units

**Total quantities in the mixture:**
- Total Water = 25+89=2×9+8×545=18+4045=5845\displaystyle \frac{2}{5} + \frac{8}{9} = \frac{2 \times 9 + 8 \times 5}{45} = \frac{18 + 40}{45} = \frac{58}{45} units
- Total Milk = 35+109=3×9+10×545=27+5045=7745\displaystyle \frac{3}{5} + \frac{10}{9} = \frac{3 \times 9 + 10 \times 5}{45} = \frac{27 + 50}{45} = \frac{77}{45} units

The question asks for the ratio of **milk to water** in the resulting mixture:
Ratio of Milk : Water=Total MilkTotal Water=77455845=7758=77:58\text{Ratio of Milk : Water} = \frac{\text{Total Milk}}{\text{Total Water}} = \frac{\frac{77}{45}}{\frac{58}{45}} = \frac{77}{58} = 77:58
This matches **Option B**.
Hence, **Option B** is the correct answer.

About This Chapter: Ratio, Proportion, Indices, Logarithm

Paper

Paper 3: Quantitative Aptitude

Weightage

5-7 Marks

Key Topics

Ratio, Proportion, Indices, Logarithms

This chapter covers Ratio, Proportion, Indices, Logarithms and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 5-7 Marks weightage. Focus on understanding core concepts rather than memorizing.

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