We will learn how to divide a number into two parts in a given ratio (i.e., dividing into a given ratio).
Let the number be M. It is to be divided into two parts in the ratio a : b.
The two parts are x and y if x + y = M ........................... (i)
and \(\frac{x}{y}\) = \(\frac{a}{b}\) ........................... (ii)
From (ii), \(\frac{x}{a}\) = \(\frac{y}{b}\) = k (say).
Then , x = ak, y = bk
Substituting in (i), ak + bk = M
⟹ (a + b)k = M
⟹ k = \(\frac{M}{a + b}\)
Therefore, x = ak = \(\frac{a}{a + b}\) M and y = bk = \(\frac{b}{a + b}\) M
Two parts of M in the ratio a : b are \(\frac{aM}{a + b}\) and \(\frac{bM}{a + b}\)
Solved examples on dividing a number into a given ratio:
1. Divide 60 into two parts in the ratio 2 : 3.
Solution:
The two parts are \(\frac{2}{2 + 3}\) × 60 and \(\frac{3}{2 + 3}\) × 60
i.e., \(\frac{2}{5}\) × 60 and \(\frac{3}{5}\) × 60
i.e., 24 and 36
2. Divide 75 into two parts in the ratio 8 : 7
Solution:
The two parts are \(\frac{8}{8 + 7}\) × 75 and \(\frac{7}{8 + 7}\) × 75
i.e., \(\frac{8}{15}\) × 75 and \(\frac{7}{15}\) × 75
i.e., 40 and 35
● Ratio and proportion
10th Grade Math
From Dividing into a Given Ratio to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.