Question

(a) Two numbers are in the ratio 7:11. If 7 is added to each of the numbers find ratio
becomes 1:2. Find the number​

Answer 1

Step-by-step explanation:

ratio = 7:11

let the common multiple be x

therefore nos are 7x and 11x

if 7 added....ratio = 1:2

let the common multiple be y

therefore new nos are 1y and 2y

therefore 7x+7=1y

11x+7=2y

NOW SOLVE THESE EQUATIONS BY ELIMINATION OR SUBSTITUTION OR CROSS MULTIPLIVATION

Answer 2

★ Given :-

2 no's are in ratio 7:11

7 is added to these no's then the ratio 1:2

★ To find :-

Both the Numbers ?

★ Solution :-

Let,

1st number = 7x

2nd number = 11x

Equation :-

$⟹ \ \boxed{ \bf \red{\frac{7x + 7}{11x + 7} = \frac{1}{2} }}$

By Cross multiplication

$⟶ \: \bf2(7x - 7) = 1(11x + 7)$

$⟶ \bf14x+14 = 11x+7$

$\bf⟶3x = - 7$

$\large \bf ⟶ \red{x = \frac{ - 7}{3} }$

Hence,

$\star \: \purple{ \sf\underline{First \: number }}: -$

$⟼ \boxed{ \bf7x = \small \frac{ - 7}{3} × { 7} = \small \frac{49}{3} }$

$\star \: \purple{ \sf\underline{Second \: number }}: -$

$⟼ \boxed{ \bf11x = \small \frac{ - 7}{3} × { 11} = \small \frac{ - 77}{3} }$