The numerator of a fraction is 7 less than its denominator. If the denominator is increased by 9 and the numerator by 2, the fraction becomes 23. Find the fraction.
2533
3325
2633
3326
A
3325
B
3326
C
2533
D
2633
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Solution
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Let the numerator be x and
the denominator be y
Given that numerator of a fraction is 7 less than its denominator
Therefore, x+7=y ------(1)
Given that if the denominator increased by 9 and the numerator by 2 then the fraction is 23
Therefore, x+2y+9=23
⟹3x+6=2y+18
⟹3x−2y=12
⟹3x−2(x+7)=12
⟹x−14=12
⟹x=26
⟹y=26+7=33 (from (1))
Therefore, the fraction is 2633
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