Question

The denominator of a rational number is greater than its numerator by 4. If the numerator is increased by 7 and the denominator is decreased by 2, the new number becomes 6/5. find the original rational number. ​

Answer 1

let the numerator = x

So, denominator=-x+4

Number=x+4x

 According to question, 

 x+4−1x+11=37

⟹3(x+11)=7(x+3)

⟹4x=12

⟹x=3

Hence, original number =73

Answer 2

Answer:

The number is $\frac{23}{27}$

Step-by-step explanation:

Let the number in the numerator be 'n'

and the number in the denominator be 'd'

According to the given conditions in the question,

d = n + 4                      -- (i)

and   $\frac{n+7}{d-2}$ = $\frac{6}{5}$                -- (ii)

On solving, $\frac{n+7}{d-2}$ = $\frac{6}{5}$

=> 5 ( n + 7 ) = 6 ( d - 2)

=> 5n + 35 = 6d - 12

=> 5n - 6d = -12 - 35

=> 5n - 6d = -47                    -- (iii)

Multiplying equation (i) by 5, we get 5d = 5n + 20

=>  - 5n + 5d = 20                   -- (iv)

Solving equation (iii) and (iv), we get

=> -d = -27

=> d = 27

Since n = d - 4           (from equation (i))

=> n = 27 -4

=> n = 23

Therefore, the number is $\frac{23}{27}$