Divide 1400 into three part such that the 1st part is 2/3 of 2nd part and the ratio between the 2nd and 3rd part is 4:5. Find each part.

The ratio is defined as the relation between the quantities of two or more objects and it indicates the amount of one object contained in the other.

Answer: The three parts of the number 1400 where the 1st part is 2/3 of 2nd part and the ratio between the 2nd and 3rd part is 4:5 are 320, 480, and 600.

The general form of representing a ratio of two quantities say 'a' and 'b' is a : b.

Explanation:

Let's assume the 1st part, 2nd part and the 3rd part be 'x', 'y', and 'z'.

Since, the 1st part is 2/3 of 2nd part, therefore x = (2/3) y.

Now, it is also given that the ratio between the 2nd and 3rd part is 4:5, therefore y/z = 4/5.

Now, use the equation y/z = 4/5 and calculate the value of 'z' in terms of 'y':

y/z = 4/5

⇒ 4z = 5y

⇒ z = (5/4)y

As the sum of all the three parts is equal to 1400,

⇒ x + y + z = 1400

⇒ (2/3) y + y + (5/4)y = 1400

⇒ ((8+12+15)/12)y = 1400

⇒ (35/12) y =1400

⇒ y= (1400 × 12)/35

⇒ y = 480

Now, substitute y = 480 in the equation x = (2/3) y to calculate the first number.

x = (2/3) × 480

⇒ x = 320

Now substitute y = 480 in the equation z = (5/4)y to calculate the third number.

z = (5/4) × 480

⇒ z = 600

Therefore, the three parts of 1400 are 320, 480, and 600.