In a rational number, twice the numerator is 2 more than the denominator . If 3 is added to each , the numerator and the denominator , the new fraction is 2/3. Find the original number.
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Let x be the numerator and y be the denominator of the number. Then according to the question,
2x=y+2
or, 2x-y=2 -----------------(1)
x+3/y+3=2/3
or, 3x+9=2y+6
or, 3x-2y=6-9
or, 3x-2y=-3 ----------------(2)
Multiplying (1) with 2 and (2) with 1 we get,
4x-2y=4
3x-2y=-3
Subtracting we get,
x=7
Putting in (1) we get,
2×7-y=2
or, 14-y=2
or, -y=2-14
or, -y=-12
or, y=12
∴, the original number is 7/12.
2x=y+2
or, 2x-y=2 -----------------(1)
x+3/y+3=2/3
or, 3x+9=2y+6
or, 3x-2y=6-9
or, 3x-2y=-3 ----------------(2)
Multiplying (1) with 2 and (2) with 1 we get,
4x-2y=4
3x-2y=-3
Subtracting we get,
x=7
Putting in (1) we get,
2×7-y=2
or, 14-y=2
or, -y=2-14
or, -y=-12
or, y=12
∴, the original number is 7/12.
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