# 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.

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