Find the fraction which is equal to 1/2 when both it's numerator and denominator are increased by 2. IT is equal to 3/4 when both are increased by 12.
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Answer:
Required Fraction:3/8
Step-by-step explanation:
Let the numerator be equal to x and the denominator be equal to y,
∴ Required fraction = x/y
ATQ, x+2/y+2 = 1/2 ------------ (1)
x+12/y+12=3/4 -------------(2)
Solving (1) and (2),
2x+4 = y+2
2x+2 = y -------------(3)
Substitute (3) in (2)
x+ 12/2x+2+12=3/4
x+12/2x+14 = 3/4
4x + 48 = 6x + 42
48-42 = 6x-4x
6=2x
6/2 = x
3 = x
⇒ y=2(3) +2 = 6+2 = 8
Hence, Required fraction = 3/8
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