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

Explanation

Given A:B = 3:4 and B:C = 12:13.

First, make the ratios for B consistent:

A:B = 3:4 = 9:12 (multiplied by 3)

Now, B:C = 12:13

A:B:C = 9:12:13

A:C = 9:13

Last verified on 17-06-2026

Explanation

Shaded portion = 4 out of 12 = 4/12 = 1/3 of the circle.

Total students = 2400  

Freshman students = 2400 × (4/12)  

= 2400 × (1/3)  

= 800

The freshman class has 800 students.

Last verified on 26-05-2026