Explanation

• A ratio is the comparison of two quantities.
• It shows how much of one quantity exists compared to another.
• Ratios are usually written as a:b or a/b.
• Both quantities should be expressed in the same units.
• Ratios are widely used in mathematics, science, and everyday life.

Last verified on 12-07-2026

Explanation

Initial ratio A : B = 3 : 4  

Let A = 3x, B = 4x  

A is increased by 20%  

New A = 3x + 20% of 3x = 3x + 0.6x = 3.6x  

B is increased by 10%  

New B = 4x + 10% of 4x = 4x + 0.4x = 4.4x  

New ratio = 3.6x : 4.4x = 36 : 44  

Divide by 4:  

36 / 4 : 44 / 4 = 9 : 11

Last verified on 09-07-2026

Explanation

Initial ratio milk : water = 4 : 1

Let initial milk = 4x  

Let initial water = x  

Total = 5x  

10 liters of mixture taken out.  

In the mixture, milk = 4/5 and water = 1/5  

Milk taken out = 10 × 4/5 = 8 liters  

Water taken out = 10 × 1/5 = 2 liters  

Remaining:  

Milk = 4x - 8  

Water = x - 2  

Now 10 liters of water is added.  

New Water = x - 2 + 10 = x + 8  

New Milk = 4x - 8  

New ratio milk : water = 2 : 3  

So,  

(4x - 8) / (x + 8) = 2 / 3  

Cross multiply:  

3(4x - 8) = 2(x + 8)  

12x - 24 = 2x + 16  

12x - 2x = 16 + 24  

10x = 40  

x = 4  

Original milk = 4x = 4 × 4 = 16 liters

Last verified on 09-07-2026

Explanation

Let milk = 5x  

Let water = x  

Initial ratio milk : water = 5 : 1  

After adding 12 liters water:  

Milk = 5x  

Water = x + 12  

New ratio milk : water = 5 : 3  

So,  

5x / (x + 12) = 5 / 3  

Cross multiply:  

5x _ 3 = 5 _ (x + 12)  

15x = 5x + 60  

15x - 5x = 60  

10x = 60  

x = 6  

Milk = 5x = 5 * 6 = 30 liters

Last verified on 09-07-2026

Explanation

Numbers are multiples of 6, and first number after A is 18  

So the numbers are: 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84  

That’s 12 numbers total  

Last number = 18 + (12-1)×6 = 18 + 66 = 84  

B comes right after the last number, and B also must be a multiple of 6  

Next multiple of 6 after 84 is 84 + 6 = 90  

Last verified on 21-06-2026