Ten years ago, the age of mother was three times the age of her son. after ten years, mother’s age will be twice that of his son. find the ratio of their present ages

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1

ten years ago, the age of mother was three times the age of her son. after ten years, mother’s age will be twice that of his son. find the ratio of their present ages.

2

To find the ratio of their present ages, we need to solve the problem step by step.

Let’s represent the present age of the mother as “M” and the present age of the son as “S”.

According to the first piece of information, “ten years ago, the age of the mother was three times the age of her son.” So we can write the equation:

M - 10 = 3(S - 10)

Expanding the equation, we have:

M - 10 = 3S - 30

Simplifying further:

M = 3S - 20 —(Equation 1)

Now, according to the second piece of information, “after ten years, the mother’s age will be twice that of her son.” So the equation becomes:

M + 10 = 2(S + 10)

Expanding the equation:

M + 10 = 2S + 20

Simplifying further:

M = 2S + 10 —(Equation 2)

Now we have a system of two equations (Equation 1 and Equation 2) with two variables (M and S). We can solve this system of equations to find the values of M and S.

Substituting Equation 2 into Equation 1, we get:

2S + 10 = 3S - 20

Rearranging terms:

3S - 2S = 10 + 20

Simplifying:

S = 30

Now, substitute the value of S back into Equation 2 to find the value of M:

M = 2(30) + 10 = 70

Therefore, the present ages of the mother and son are 70 and 30, respectively.

To find the ratio of their present ages, we divide the mother’s age by the son’s age:

Ratio of present ages = M/S = 70/30 = 7/3

So, the ratio of their present ages is 7:3.

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