Question 1119161
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If the woman is 15 years older than her daughter, then when the ratio of their ages was 4:1 their ages had to be 20 and 5.  That was 10 years ago; so now the mother is 30 and the daughter is 15.<br>
There was a bit of mental arithmetic there....<br>
If the ratio of two numbers is 4:1, then the two numbers can be represented by 4x and x; the difference between the two numbers is then 4x-x = 3x.  Since the difference in ages is 15, 3x=15 so x=5.  Then the ages (10 years ago) were x=5 and 4x=20; the current ages are 5+10=15 and 20+10=30.