The sum of the numerator and denominator of a fraction is 4 than twice the numerator. if the numerator and denominator are increased by 3 they are in the ratio 2:3 deter mine the fraction
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Let the required fraction be x/y .
As per the question
x + y = 4 + 2x
⇒ y – x = 4 ……(i)
After changing the numerator and denominator
New numerator = x + 3
New denominator = y + 3
Therefore x+3/ y+3 = 2/3
⇒3(x + 3) = 2(y + 3)
⇒3x + 9 = 2y + 6
⇒ 2y – 3x = 3 ……(ii)
Multiplying (i) by 3 and subtracting (ii), we get:
3y – 2y = 12 – 3 ⇒y = 9
Now, putting y = 9 in (i), we get:
9 – x = 4 ⇒ x = 9 – 4 = 5
Hence, the required fraction is 5/9
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Step-by-step explanation:
in an AP: if a=5 and d=1/4 write the first four terms
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