# Dividing a Quantity in Three given Ratios

Rules of dividing a quantity in three given ratios is explained below along with the different types of examples.

If a quantity K is divided into three parts in the ratio X : Y : Z, then

First part = X/(X + Y + Z) × K,

Second part = Y/(X + Y + Z) × K,

Third part = Z/(X + Y + Z) × K.

For example, suppose, we have to divide $1200 among X, Y, Z in the ratio 2 : 3 : 7. This means that if X gets 2 portions, then Y will get 3 portions and Z will get 7 portions. Thus, total portions = 2 + 3 + 7 = 12. So, we have to divide$ 1200 into 12 portions and then distribute the portions among X, Y, Z according to their share.

Thus, X will get 2/12 of $1200, i.e., 2/12 × 1200 =$ 200

Y will get 3/12 of $1200, i.e., 3/12 × 1200 =$ 300

Z will get 7/12 of $1200, i.e., 7/12 × 1200 =$ 700

Solved examples:

1. If $135 is divided among three boys in the ratio 2 : 3 : 4, find the share of each boy. Solution: The sum of the terms of the ratio = 2 + 3 + 4 = 9 Share of first boy = 2/9 × 135 =$ 30.

Share of second boy = 3/9 × 315 = $45. Share of first boy = 4/9 × 315 =$ 60.

Thus, the required shares are $30,$ 45 and \$ 60 respectively.

2. Divide 99 into three parts in the ratio 2 : 4 : 5.

Solution:

Since,  2 + 4 + 5 = 11.

Therefore, first part = 2/11 × 99 = 18.

Second part = 4/11 × 99 = 36.

And, third part = 5/11 × 99 = 45.

3. 420 articles are divided among A, B and C, such that A gets three-times of B and B gets five-times of C. Find the number of articles received by B.

Solution:

Let the number of articles C gets = 1

The number of article that B gets = five times of C = 5 × 1 = 5.

And, the number of articles that A gets = three times of B = 3 × 5 = 15.

Therefore, A : B : C = 15 : 5 : 1

And, A + B + C = 15 + 5 + 1 = 21

The number of articles received by B = 5/21 × 420 = 100

The above examples on dividing a quantity in three given ratios will help us to solve different types of problems on ratios.

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