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Question

In a fraction, if numerator is increased by 2 and denominator is decreased by 3, then the fraction becomes 1. Instead, if numerator is decreased by 2 and denominator is increased by 3, then the fraction becomes 38. Find the fraction.

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Solution

Let the fraction be ab.

Therefore, a+2b3=1

a+2=b3

ab=5 .......(1)

Also, a2b+3=38

8a16=3b+9

8a3b=25

Solving these equations, we get,

a=8 and b=13

Thus, the fraction is 813.
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