Question

14 a and b part please class 10​

Answer 1

a.

Let the numerator be x.

Let the denominator be y.

Let the fraction be x/y

The denominator is one less than three times the numerator.

y = 3x - 1

3x - y = 1

Let the above equation be equation 1.

On adding 1 to the numerator, the fraction becomes 1/2

$\dfrac{x + 1}{y} = \dfrac{1}{2} \\ \\ x + 1 = \frac{y}{2} \\ \\ 2(x + 1) = y \\ \\ 2x + 2 = y \\ \\y - 2x = 2$

Let the above equation be equation 2.

Adding equations 1 and 2.

$(3x - y) + (y - 2x)= 1 + 2 \\ \\ 3x - y + y - 2x = 3 \\ \\ 3x - 2x = 3 \\ \\ x = 3$

The numerator is 3.

Substitute x= 3 in equation 2.

$y - 2x = 2 \\ \\ y - (2 \times 3) = 2 \\ \\ y - 6 = 2 \\ \\ y = 2 + 6 \\ \\ y = 8$

The denominator is 8.

The denominator is 8.The fraction is 3/8

b.

Let the numerator be x.

Let the denominator be y.

Let the fraction be x/y

The denominator is 4 more than twice the numerator.

y = 4 + 2x

y - 2x = 4

Let the above equation be equation 1.

Denominator decreased by 6 is equal to 12 times the numerator decreased by 6.

$y - 6 = 12(x - 6) \\ \\ y - 6 = 12x - 72 \\ \\ 72 - 6 = 12x - y \\ \\ 12x - y = 66$

Let the above equation be equation 2.

Adding equations 1 and 2.

$(y - 2x ) + (12x - y)= 4 + 66 \\ \\ y - 2x + 12x - y = 4 + 66 \\ \\ 10x = 70 \\ \\ x = \frac{70}{10} \\ \\ x = 7$

The numerator is 7.

Substitute x= 7 in equation 1.

$y - 2x = 4 \\ \\ y - (2 \times 7) = 4 \\ \\ y - 14 = 4 \\ \\ y = 4 + 14 \\ \\ y = 18$

The denominator is 18.

The denominator is 18.The fraction is 7/18.