Question

In a rational number the denominator exceeds the numerator by 4.if the numerator and denominator are increased by 9 the rational number becomes 7/8 . Find the original number

Answer 1

Given that,

in a rational number, the denominator is 4 more than it's numerator.

let the numerator of the rational number be x.

therefore it's denominator = x + 4

ATQ, when both denominator and numerator are increased by 9, then the rational number becomes 7/8

➡ (x + 9)/(x + 4 + 9) = 7/8

➡ (x + 9)/(x + 13) = 7/8

by cross multiplication, we get

➡ 8(x + 9) = 7(x + 13)

➡ 8x + 72 = 7x + 91

➡ 8x - 7x = 91 - 72

➡ x = 19

therefore,

• numerator = x = 19

• denominator = x + 4 = 23

hence, the original number is 19/23

VERIFICATION :-

LHS -

= (x + 9)/(x + 13)

= (19 + 9)/(19 + 13)

= 28/32 = 7/8

RHS -

= 7/8

LHS = RHS. hence verified!

Answer 2

Answer:

19/23

Step-by-step explanation:

in a rational number, the denominator is 4 more than it's numerator.

let the numerator of the rational number be x.

therefore it's denominator = x + 4

ATQ, when both denominator and numerator are increased by 9, then the rational number becomes 7/8

➡ (x + 9)/(x + 4 + 9) = 7/8

➡ (x + 9)/(x + 13) = 7/8

by cross multiplication, we get

➡ 8(x + 9) = 7(x + 13)

➡ 8x + 72 = 7x + 91

➡ 8x - 7x = 91 - 72

➡ x = 19

therefore,

numerator = x = 19

denominator = x + 4 = 23

hence, the original number is 19/23

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