Question

The denominator of a rational number is greater than its numerator by 7. if 3 is subtracted from the numerator and 2 is added to its denominator,the new number becomes 1/5.Find therational number

Answer 1

Let rational no be A/B

B = A + 7

Now

A-3)/B +2 = 1/5

A- 3)/ A+ 9 = 1/5

Apply componendo and dividendo

A- 3+ A + 9)/ A- 3 - A - 9. = 1+5)/ 1 -5

2A + 6)/ -12 = -6/4

-A-3)/ 6 = -3/2

A+3)/6 = 3/2

A+ 3 = 9

A= 6

so rational no is A/(A+7) = 6/ (6+7) = 6/13


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Answer 2

LET numerator be =x
Then Denominator=x+7

If 3 is subtracted from numerator and 2 added to Denominator=1/5

A/Q
$\frac{x - 3}{x + 7 + 2} = \frac{1}{5} \\ = \frac{x - 3}{x + 9} = \frac{1}{5} \: (by \: cross \: multiplication) \\ = 5(x - 3) = x + 9 \\ = 5x - 15 = x + 9 \\ 5x - x = 9 + 15 \\ 4x = 24 \\ x = \frac{24}{4} \\ x = 6$
So Numerator=6
Denominator=6+7=13

Rational Number=6/13