Question

The numerator and the denominator of a rational number are in the ratio 5 : 7. When 6 is added to both the numerator and denominator, the ratio becomes 4 : 5. What is the rational number?

Answer 1

Answer:

LET THE NUMERATOR AND DENOMINATOR BE 5X,7X

ATQ

5X+6/7x+6=4/5

5(5X+6)=4(7X+6)

25X+30=28X+24

25X-28X=24-30

-3X=-6

X=2

THEREFORE NO. ARE

NUMERATOR = 5*2=10

DENOMINATOR=7*2=14

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Step-by-step explanation:

Answer 2

Given - Ratio

Find - Rational number

Solution - Let the numerator and denominator of rational number be 5x and 7x. Representing the given information in mathematical expression -

$\frac{5x + 6}{7x + 6} = \frac{4}{5}$

Performing cross multiplication

$(5x + 6) \times 5 = (7x + 6) \times 4$

Performing multiplication

$25x + 30 = 28x + 24$

Shifting values and performing subtraction

$30 - 24 = 28x - 25x$

$6 = 3x$

Shifting 3 to other side of equation and performing division

$x = \frac{6}{3}$

$x = 2$

Numerator = 5x

Numerator = 5*2

Performing multiplication

Numerator = 10

Denominator = 7x

Denominator = 7*2

Performing multiplication

Denominator = 14

Rational number = $\frac{10}{14}$

Performing division by 2

Rational number = $\frac{5}{7}$

Hence, the ration number is 5/7.