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Initial Ratio (W:M) = 3 : 2 (Total = 5 units) | Final Ratio (W:M) = 1 : 2 (Total = 3 units)

Since only Milk is added, Water remains constant. Make Water units same: (3:2) and (1:2)×3 → (3:2) and (3:6).

Milk increase = 6 − 2 = 4 units. This 4 units = 5 liters replaced. So, 1 unit = 1.25 liters.

Total capacity = 3 + 6 = 9 units = 9 × 1.25 = 11.25 liters. Initial Milk = (2/5) × 11.25 = 4.5 liters.

∴ The correct answer is 4.5 liters.

Alternate Method

Given: Initial ratio Water : Milk = 3 : 2. Replaced volume = 5 liters. Final ratio = 1 : 2.

Formula Used: Quantity of liquid = Total volume × (Ratio part / Total parts)

⇒ Let total initial volume be 5x. Water = 3x, Milk = 2x.

⇒ After removing 5L: Water = 3x − 5×(3/5) = 3x − 3; Milk = 2x − 5×(2/5) = 2x − 2.

⇒ Adding 5L pure Milk: New Milk = 2x − 2 + 5 = 2x + 3.

⇒ New Ratio: (3x − 3) / (2x + 3) = 1 / 2

⇒ 2(3x − 3) = 1(2x + 3) ⇒ 6x − 6 = 2x + 3 ⇒ 4x = 9 ⇒ x = 2.25.

⇒ Initial Milk = 2x = 2 × 2.25 = 4.5 liters.

∴ The correct answer is 4.5 liters.

Additional Information

Mixture Replacement Rule

When a portion of mixture is removed, the ratio of components in the remaining mixture stays the same as the initial ratio.

Alligation Method for Replacement

Concentration of milk in original × (Volume left) + Concentration of added milk × (Volume added) = Final concentration × Total Volume.

Follow BODMAS rule to solve this question, as per the order given below

⇒ 987 + 23% of 1500 = ? + 21% of 700

$\Rightarrow 987 + \frac{{23}}{{100}} \times 1500 = ;? + \frac{{21}}{{100}} \times 700$

⇒ 987 + 23 × 15 = ? + 21 × 7

⇒ 987 + 345 = ? + 147

⇒ 1332 = ? + 147

⇒ ? = 1332 – 147 = 1185

⇒ ? = 1185

Follow BODMAS rule to solve this question, as per the order given below,

Step - 1 - Parts of an equation enclosed in 'Brackets' must be solved first, and in the bracket,

Step - 2 - Any mathematical 'Of' or 'Exponent' must be solved next,

Step - 3 - Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step - 4 - Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Given expression is,

⇒ 271 + 85 × 3 – 122 = ? + 36 × 9

⇒ 271 + 255 – 122 = ? + 36 × 9

⇒ 526 – 122 = ? + 324

⇒ ? = 404 – 324

∴ ? = 80

Concept used:

Calculation:

Given expression is,

3 – [19 + {14 – (16 – 3 – 21)}]=?

⇒ 3 – [19 + {14 – (13 – 21)}] =?

⇒ 3 – [19 + {14 – (- 8)}] =?

⇒ 3 – [19 + {14 + 8}] =?

⇒ 3 – [19 + 22] =?

⇒ 3 – [41] =?

⇒ ? = -38

∴ The value of ? is -38

Concept used:

Follow BODMAS rule to solve this question, as per the order given below:

The given expression is,

(42 – 23) × 6 – 5 × (4² + 5)

= 19 × 6 – 5 × (16 + 5)

= 19 × 6 – 5 × 21

= 114 – 105

= 9

Concept used:

Follow BODMAS rule to solve this question, as per the order given below,

Calculation:

599 – 339 + 459 – 319 = ?2 

599 + 459 – (339 + 319) = ?2

1058 – 658 = 400 = ?2

? = √400 = 20

∴ The value of ?' is 20

Given

The value is 3-2 × 272/3 ÷ (729)-1/3

Calculation

3-2 × 272/3 ÷ (729)^-1/3

⇒ (1/3²) × (3³)^2/3 ÷ (9³)^-1/3

⇒ (1/9) × 32 ÷ 1/9

⇒ (1/9) × 9 × 9

⇒  9

∴ the value of 3-2 × 272/3 ÷ (729)^-1/3 is 9

Given:

[90 ÷ 6 × (24 - 8 ÷ 4) ÷ 3] – 90 ÷ 5 + 34

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

Using the BODMAS rule

⇒ [90 ÷ 6 × (24 – 8 ÷ 4) ÷ 3] – 90 ÷ 5 + 34 = ?

⇒ [90 ÷ 6 × (24 – 2) ÷ 3] – 90 ÷ 5 + 34 = ?

⇒ [90 ÷ 6 × (22) ÷ 3] – 90 ÷ 5 + 34 = ?

⇒ [90 ÷ 6 × 22/3] – 90 ÷ 5 + 34 = ?

⇒ [15 × 22/3] – 90 ÷ 5 + 34 = ?

⇒ [110] – 90 ÷ 5 + 34 = ?

⇒ 110 – 18 + 34 = ?

⇒ 110 + 16 = ?

⇒ ? = 126

∴ In place of ‘?’ 126 will come in place of ‘?’

Concept used:

Follow BODMAS rule to solve this question, as per the order given below:

Calculation:

⇒ 2487 + 4876 – 5645 + 222 = ?

⇒ 7363 – 5645 + 222 = ?

⇒ 1718 + 222 = ?

⇒ ? = 1940

∴ The value of ? is 1940

Calculations:

Considering the given equation,

(27)2 – (13)2 + (12)3 + (23)2 = ?

⇒ 729 – 169 + 1728 + 529 = ?

⇒ 2817 = ?

∴ The value of ? is 2817.