the numerator of a fraction is 4 less than its denominator if 3 is added to the numerator and 2 is subtracted to the denominator the fraction becomes 3/5. what is fraction.
Answers
Answer:
Step-by-step explanation:
The numerator of a given fraction is 4 lessthan its denominator. If 3 is subtracted from the numerator and 5 is added to the denominator, the resulting fraction becomes one-fourth .
TO FIND :
The fraction for the given condition.
SOLUTION :
Given that the numerator of a given fraction is 4 less than its denominator.
Also given that 3 is subtracted from the numerator and 5 is added to the denominator, the fraction becomes one by fourth .
Let the fraction be
Since the numerator of a given fraction is 4 less than its denominator we have,
Numerator=Denominator-4
⇒ a=b-4
Since 3 is subtracted from the numerator and 5 is added to the denominator, the fraction becomes one by fourth we have
4(a-3)=1(b+5)
4a-12=b+5
4a-b=17
4(b-4)-b=17 ( ∵ a=b-4)
4b-16-b=17
3b=17+16
3b=33
⇒ b=11
Now put b=11 in a=b-4 we get
a=11-4
⇒ a=7
∴ the fraction is