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Answer:
Year 2030.
Step-by-step explanation
In 1997, Let Tim's age = <em>X</em> years
In 1997, Let Sue's age = <em>Y</em> years
After 5 years in 2002, Tim's age = (<em>X+ 5) </em>years
After 5 years in 2002, Sue's age = <em>(Y + 5)</em> years
Now, According to question,
<em>X </em>+ <em>Y</em> = 32 (sum of their ages) .......(1)
<em>Y </em>= 32 -<em> X</em>
(X + 5) = 2 (Y + 5) .......(2)
Substituting the value of <em>Y</em> in (2)
<em>X </em>+ 5 = 2 (32 - <em>X </em>+ 5)
<em>X </em>+ 5 = 2 (37 - <em>X </em>)
<em>X </em>+ 5 = 74 - 2<em>X </em>
3<em>X </em>=<em> </em>69
<em>X </em>= 69/3 = 23
Now ∵<em> Y</em> = 32 - <em>X </em>and<em> X = </em>23
∴ <em>Y</em> = 32 - 23 = 9
So, In 1997, Tim's age = 23 years and Sue's age = 9 years.
Let the year in which Sue's age will be three-fourth times of Tim's age be t.
Sue's age after<em> t </em>years = (9 +<em> t) </em>years.
Tim's age after<em> t</em> years = (23 + <em>t</em>) years
According to question,
<em></em>
<em></em>
The Year in which Sue's age will be three-fourth times of Tim's age is:
= (1997 + 33) = 2030.