Question

5. The denominator of a rational number is greater
than its numerator by 7. If the numerator is
increased by 17 and the denominator is decreased
by 6, the new number becomes 2. Find the
original number
​

Answer 1

Step-by-step explanation:

Let us take the numerator to be x.

So, the denominator will be x+7.

Given condition is

The numerator when increased by 17 = x+17

and the denominator when decreased by 6 =x+7-6 =x+1

Then, this must be equal to 2.

x+17 = 2

x+1

(x+17) = 2(x+1)

x+17 = 2x+2

2x-x = 17-2

x = 15

Thus, the numerator = x = 15.

As per the condition, the denominator is greater than its numerator by 7.

And, the denominator = x+7 = 15+7 = 22

So, the fraction is =15/22

Thus, the original number is the fraction of 15/22