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# A number is divided into two parts such that one part is six more than the other. If the two parts are in a ratio $6:5$, find the small part.

**Given :**

A number is divided into two parts such that one part is six more than the other.

The two parts are in the ratio of $6:5$.

**To find :**

We have to find the small part.

**Solution :**

Let the two parts be $6x$ and $5x$.

This implies,

$6x = 5x+6$

$6x-5x = 6$

$x = 6$

The two parts are $5(6)=30$ and $6(6)=36$.

**The smaller part is $30$.**

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