Explanation

6(A's Capital) = 8(B's Capital) = 10(C's Capital)

We can write this as:

A's Capital = x

B's Capital = x × (6/8) = 0.75x

C's Capital = x × (6/10) = 0.6x

Now, we can write the ratio of their capitals as:

A's Capital : B's Capital : C's Capital = x : 0.75x : 0.6x

Divide each term by x:

A's Capital : B's Capital : C's Capital = 1 : 0.75 : 0.6

Multiply each term by 20 (the least common multiple of 1, 0.75, and 0.6) to eliminate decimals:

A's Capital : B's Capital : C's Capital = 20 : 15 : 12

So, the ratio of their capitals is:

20 : 15 : 12

Explanation

To divide Rs. 2000 in the ratio 3:2, we need to first calculate the total number of shares:

3 + 2 = 5

Then, we divide the total amount (Rs. 2000) by the total number of shares (5):

Rs. 2000 ÷ 5 = Rs. 400

Now, we multiply the share value (Rs. 400) by the respective ratio numbers to find the two shares:

Share 1 (3): 3 × Rs. 400 = Rs. 1200

Share 2 (2): 2 × Rs. 400 = Rs. 800

So, the two shares are Rs. 1200 and Rs. 800.

Explanation

To solve this proportion, we can use the following steps:

Write the proportion as a fraction: 3/x = 12/20

Cross-multiply: 3 × 20 = 12 × x

Simplify: 60 = 12x

Divide both sides by 12: x = 60/12

Simplify: x = 5

So, the value of x is 5.

Explanation

The total number of students in the school is 360 boys + 240 girls = 600 students.

The ratio of the number of boys to the total number of students is 360/600 = 3/5.

This can also be written as a fraction as 3:5 or as a decimal as 0.6.

Explanation

Initially, the milkman has 10 liters of milk and adds 10 liters of water, making the total solution 20 liters (10 milk + 10 water).

The ratio of milk to water is 1:1, so the concentration of milk is 50% (10 liters milk / 20 liters total).

The son takes 15 liters of this solution, which contains 50% milk, so he takes 7.5 liters of milk (15 liters x 0.5) and 7.5 liters of water.

The son then adds 5 liters of water to the 15 liters he took, making the total solution 20 liters again (7.5 milk + 7.5 water + 5 water).

Now, the total water in the solution is 7.5 liters (initial water) + 5 liters (added water) = 12.5 liters.

So, the amount of water in the milk is 12.5 liters.