Question 67

A fraction is such that the numerator is five less than the denominator. Also four times the numerator is one more than the denominator. The fraction is:

Solution

Let's assume the fraction is $$\frac{P}{Q}$$.
A fraction is such that the numerator is five less than the denominator.

P = Q-5

Q = P+5 Eq.(i)

Also four times the numerator is one more than the denominator.

4P = Q+1 Eq.(ii)

Put the value of 'Q' from Eq.(i) to Eq.(ii).

4P = P+5+1

4P-P = 6

3P = 6

P = 2

Put the value of 'P' in Eq.(i).

Q = P+5 = 2+5 = 7

fraction = $$\frac{P}{Q}\ =\ \frac{2}{7}$$

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