Question

the numorator of a fraction is 4 less than its denominator if the number is decreased by 2 and denominator is increased by 1 the denominator becomes 8 times is its numerator find the fraction

Answer 1

Let the required fraction be (N/D), where N= numerator and D= denominator.

By question, N = D-4........(1)

Again, (N-2)/(D+1)= N/8N......(2)

From (2), (N-2)/(D+1) = 1/8

Or, 8(N-2) = D+1

Or, 8N-16= D+1

Or, 8N-D= 17..........(3)

Using (1) in (3) we get

8(D-4) -D = 17

Or,8D-32-D =17

Or,7D =49

Therefore, D = 7.

Now, putting this value of D in (1), we get

N = D-4 = 7-4 = 3.

Therefore, required fraction is (N/D)= (3/7).