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A mother is now 2 and ahalf times old as her daughter Mary. Four years ago the ratio of their ages was 3:1. Find the present age of the mother.

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Given:

A mother is now 2 and a half times old as her daughter Mary.

Four years ago the ratio of their ages was 3:1.

To find:

The present age of the mother.

Solution:

Let x be the present age Mary's mother and y be the present age of Mary.

A mother is now 2 and a half times old as her daughter Mary. So,


x=2(1)/(2)y


(x)/(y)=(2(2)+1)/(2)


(x)/(y)=(5)/(2)

It means the ratio of their present age is 5:2. Let 5z be the present age of Mary's mother and 2z be the present age of Mary.

Four years ago the ratio of their ages was 3:1.


(5z-4)/(2z-4)=(3)/(1)


1(5z-4)=3(2z-4)


5z-4=6z-12


-4+12=6z-5z


8=z

Now, the present age of the mother is:


5z=5(8)


5z=40

Therefore, the present age of the mother is 40 years.

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