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 becomes1by5

Answer 1

Let the numerator be x and Denominator be y

so Rational number = x / y

Now, ATQ

Denominator is grater than numerator by 7

∴ y = x + 7 -----(i)

Also,

When we subtract 3 from numerator (x - 3) and

2 is added to denominator (y + 2)

New rational number we get

$\frac{(x-3)}{(y+2)}$

which is equals to 1/5

$\frac{(x-3)}{(y+2)}=\frac{1}{5}$$5(x-3) = y+2\\5x - 15 = y+2\\5x-y=17$ --- (ii)

Putting value of y from equation (i) in equation ( ii )

5x - (x+7) = 17

4x - 7 =17

4x = 24

x = 6

Putting value of x in eq ( i )

y = 6 + 7

y  = 13

Hence the desired rational number is 6 / 13

Answer 2

✬ Number or Fraction = 6/13 ✬

Step-by-step explanation:

Given:

• Denominator is greater than its Numerator by 7.
• If 3 is subtracted from the numerator and 2 is added to the denominator the new number becomes 1/5

To Find:

• What is the original number or fraction?

Solution: Let the numerator be x. Then, the denominator (x + 7).

• Fraction = x/(x + 7)

→ After subtracting 3 from the numerator.

• New Numerator = (x – 3)

→ After adding 2 to the denominator.

• New Denominator = (x + 7)+2 = (x + 9)

∴ New Fraction = n/d = (x – 3)/(x + 9)

A/q

$\implies{\rm }$ (x – 3)/(x + 9) = 1/5

$\implies{\rm }$ 5 (x – 3) = x + 9 (By cross multiplication)

$\implies{\rm }$ 5x – 15 = x + 9

$\implies{\rm }$ 5x – x = 9 + 15

$\implies{\rm }$ 4x = 24

$\implies{\rm }$ x = 24/4

$\implies{\rm }$ x = 6

∴ Numerator = x = 6 and

∴ Denominator = (x + 7) = 6 + 7 = 13

Hence, The original fraction or number is n/d = 6/13