Question

Mopa IV 7. (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

Given :

• Two numbers are in the ratio 7 : 11 .

• if 7 is added to each of the numbers .

• the ratio becomes 1 : 2

To find :

• Both the numbers = ? ?

Solution :

Let ,

• First number be 7 x

• Second number be 11 x

According to questions,

$\sf : \implies Equation = { \dfrac{7x + 7}{11x + 7} = \dfrac{1}{2}}$

by cross multiplication,

$\sf : \implies 2(7x + 7) = 1(11x + 7)$

$\sf :\implies 14x + 14= 11 x +7$

$\sf : \implies 14x + - 11x = 14-7$

$\sf : \implies 3x = - 7$

$\bf : \implies x =\frac{-7}{3}$

The value of x is$\frac{-7}{3}$

therefore ,

• First number (7x)=$(\frac{-7}{3})=(\frac{-49}{3})$

• Second number (11x)=$(\frac{-7}{3})=(\frac{-77}{3})$

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,

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

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

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

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