Question

Two numbers are in the ratio 2:7. If 6 is added to each of the numbers, the ratio becomes 1:3. Find the numbers.
[Solve it in terms if pairs of linear equations in two variable.]

Answer 1

Answer:

let the no. be x then ATQ,

(2x+6): (7x+6)= 1x+3x

9x+12=4x

9x-4x=-12

5x= -12

x= -12/5

two no. r 12/5×2 n 12/5×7

Answer 2

Answer:

let the numbers be x and y.

AQ,

x:y=2:7

$= > \frac{x}{y} = \frac{2}{7} \\ 7x = 2y \\ 7x - 2y = 0........(i)$

again

$\frac{x + 6}{y + 6} = \frac{1}{3} \\ 3(x + 6) = 1(y + 6) \\ 3x + 18 = y + 6 \\ 3x - y = 6 - 18 \\ 3x - y = - 12.........(ii )$

now

$(i) -2 \times ( ii )\:$

implies

$(7x - 2y) -2 \times (3x - y) = 0 - 2 \times ( - 12)$

$7x - 2y - 6x + 2y = 24\\ 7x - 6x = 24 \\ x = 24$

putting the value of x in equation (i) we have

$7x - 2y = 0 \\ 7 \times 24 - 2y = 0 \\ 168- 2y = 0 \\ - 2y = - 168 \\ y = \frac{168}{2} \\ y = 84$

hence the numbers are 24 and 84