Question

The denominator of a rational number is greater than its numerator by 7. If the numerator is increased by 6 and the denominator is decreased by 5, the new rational number obtained is 3/2. Find the original rational number.

Answer 1

6/13

Explanation:

6 + 6 = 12 3

---- ---- = ---

13 - 5 = 8 2

Answer 2

• Original Rational number is = 6/13

Explanation:

Let Numerator be : x

Denominator be : x + 7

Now,

• Numerator is increased by 6
• Denominator is decreased by 5
• the new rational number obtained is 3/2

Numerator = x + 6

Denominator = ( x + 7) - 5

According to the question,

`\displaystyle \: \sf \dashrightarrow \: (x + 6)/((x + 7) \: - 5) = \: (3)/(2)`

`\displaystyle \: \sf \dashrightarrow \: 2(x + 6) \: = 3 \{ \: (x + 7 ) - 5\} \:`

`\displaystyle \: \sf \dashrightarrow \: 2x \: + 12 \: = \: 3(x + 2)`

`\displaystyle \: \sf \dashrightarrow2x + 12 \: = 3x + 6`

`\displaystyle \: \sf \dashrightarrow \: 2x - 3x \: = \: 6 - 12`

`\: \: \: \displaystyle \: \sf \dashrightarrow \: - x \: = - 6 \\ \\ \: \: \: \: \: \: \displaystyle \: \bf \dashrightarrow \: x \: = 6`

Numerator = 6

Denominator = x + 7

= 6 + 7

= 13

Thus ,

`\: \bf { \red{ \underline{\dashrightarrow \: obtained \: rational \: number \: = \: (6)/(13) }}}`

`\pink{\rule{160pt}{5pt}}`