Question

The numerator of a given fraction is 4 less than its denominator. If 3 is subtracted from the numerator and 5 is added to the denominator, the fraction becomes one by fourth . What is the given fraction.

Answer 1

GIVEN :

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 $\frac{a}{b}$

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

$\frac{a-3}{b+5}=\frac{1}{4}$

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

$b=\frac{33}{3}$

⇒ b=11

Now put b=11 in a=b-4 we get

a=11-4

⇒ a=7

∴ the fraction is $\frac{a}{b}=\frac{7}{11}$

Answer 2

Answer:

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