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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