Question

the numerator of a rational is less than its denominater by 4 .if the numerator is multiplied by 2 and the denominator is increased by 4 the number becomes 14/15. find the origanal number. ​

Answer 1

Answer:

10/11

Step-by-step explanation:

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Answer 2

Answer:-

Let the number be x/y.

Given:

Numerator is less than the denominator by 4.

⟶ Numerator = Denominator - 4

⟶ x = y - 4 -- equation (1)

And,

If the numerator is multiplied by 2 and denominator is increased by 4 , the number becomes 14/15.

$\longrightarrow \sf \dfrac{2 \times x}{y + 4} = \dfrac{14}{15}$

Substitute the value of x from equation (1).

$\: \longrightarrow \sf \: \frac{2(y - 4)}{y + 4} = \frac{14}{15} \\ \\ \longrightarrow \sf \: \frac{2y - 8}{y + 4} = \frac{14}{15} \\ \\ \longrightarrow \sf \: 15(2y - 8) = 14(y + 4) \\ \\ \longrightarrow \sf \: 30y - 120 = 14y + 56 \\ \\ \longrightarrow \sf \: 30y - 14y = 56 + 120 \\ \\ \longrightarrow \sf \: 16y = 176 \\ \\ \longrightarrow \sf \: y = \frac{176}{16} \\ \\ \longrightarrow \boxed{ \sf \: y = 11}$

Substitute the value of y in equation (1).

⟶ x = y - 4

⟶ x = 11 - 4

⟶ x = 7

∴ The required number x/y is 7/11.