An equation is formed of two equal expressions. The present age of the mother is 45 years.
<h3>What is an equation?</h3>
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the son's present age be represented by x. Therefore, we can represent the statement "mother is twice as old as her son" as,
Son's present age = x
Mother's present age = 2 × son's age = 2x
Also, 20 years ago, the age of the mother was 10 times the age of the son. Therefore, we can write,
Son's age 20 years ago = x - 20
Mother's age 20 years ago = 2x - 20
Mother's age 20 years ago = 10 × Son's age 20 years ago
2x- 20 = 10 × (x - 20)
2x - 20 = 10x - 200
-20 + 200 = 10x - 2x
180 = 8x
x = 180/8
x = 22.5
Now, the present age of the mother is,
Mother's present age = 2x = 2 × 22.5 = 45
Hence, the present age of the mother is 45 years.
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