Answer:
Present age of Sharon is 35 years .
Step-by-step explanation:
Given,5 years back the ratio of age of Kate and Sharon was 4:3.
Let before 5 years age of kate be 4x years and age of Sharon be 3x years.
Now, present age of Kate is (4x+5) years and present age of Sharon is (3x+5) years
It is after 5 years sum of their age will be 90 years.
Now,after 5 years age of Kate will be (4x+5+5) years.
and after 5 years age of Sharon will be (3x5++5) years.
According to question,
[tex](4x + 5 + 5) + (3x +5 + 5) = 90 \\ 4x + 10 + 3x + 10 = 90 \\ 7x + 20 = 90 [/tex]
We are separating variable and constant part,
[tex]7x = 90 - 20[/tex]
We are Subtracting 10 from 90,
[tex]7x = 70 \\ x = \frac{70}{7} \\ x = 10[/tex]
Hence present age of Kate is
[tex](4 \times 10 + 5) \\ = 40 + 5 \\ = 45 \: years[/tex]
and present age of Sharon is
[tex](3 \times 10 + 5) \\ = 30 + 5 \\ = 35 \: years[/tex]
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