The average of three numbers A, B and C is x. If A is increased by 'y', B is increased by '2y' and C is increased by '3y', the average of the three numbers increases by 4. What is the value of 'y'?

To solve this problem, we need to understand that the average of a set of numbers is the sum of those numbers divided by the quantity of numbers.

1. The average of A, B, and C is x. So, we can write this as: (A + B + C) / 3 = x.

2. If we increase A by y, B by 2y, and C by 3y, the new average is x + 4. So, we can write this as: (A + y + B + 2y + C + 3y) / 3 = x + 4.

3. Simplifying the equation from step 2, we get: (A + B + C + 6y) / 3 = x + 4.

4. We know from step 1 that (A + B + C) / 3 = x. So, we can substitute this into the equation from step 3 to get: x + 6y / 3 = x + 4.

5. Simplifying this equation, we get: 2y = 4.

6. Solving for y, we find that y = 2.

So, the value of 'y' is 2.

To solve this problem, we need to understand that the average of a set of numbers is the sum of those numbers divided by the quantity of numbers.

Step 1: Write down the initial average equation. The average of A, B, and C is x, so we can write this as:

(A + B + C) / 3 = x

Step 2: Multiply both sides by 3 to get rid of the denominator:

A + B + C = 3x

Step 3: Write down the new average equation. The average of A+y, B+2y, and C+3y is x+4, so we can write this as:

(A + y + B + 2y + C + 3y) / 3 = x + 4

Step 4: Simplify and multiply both sides by 3:

A + B + C + 6y = 3x + 12

Step 5: We know from step 2 that A + B + C = 3x, so substitute 3x into the equation:

3x + 6y = 3x + 12

Step 6: Subtract 3x from both sides:

6y = 12

Step 7: Divide both sides by 6 to solve for y:

y = 12 / 6 = 2

So, the value of 'y' is 2.