Question

the ratio of two natural numbers is 5:6 , if a numbers is added to both numbers , the ratio becomes 7:8 if the larger exceeds the smaller number by 10 then the number added is​

Answer 1

AnswEr :

$\bold{Let's Assume} \begin{cases} \sf{Smaller \: No.=x} \\ \sf{Larger \: No.=(x+10)} \end{cases}$

• According to the Question Now :

⇒ Smaller No. : Larger No. = 5 : 6

⠀⠀⠀⋆ Putting the Values

⇒ x : ( x + 10 ) = 5 : 6

⠀⠀⠀⋆ By Cross Multiplication

⇒ 6 × x = 5 × ( x + 10 )

⇒ 6x = 5x + 50

⇒ 6x - 5x = 50

⇒ x = 50

◑ Smaller No. = x = 50

◑ Larger No. = (x + 10) = (50 + 10) = 60

_________________________________

Let the Number added to both be a

• According to Question Again :

⇒ Smaller No. + a : Larger No. + a = 7 : 8

⠀⠀⠀⋆ Putting the Values

⇒ ( 50 + a ) : ( 60 + a ) = 7 : 8

⠀⠀⠀⋆ By Cross Multiplication

⇒ 8 × ( 50 + a ) = 7 × ( 60 + a )

⇒ 400 + 8a = 420 + 7a

⇒ 8a - 7a = 420 - 400

⇒ a = 20

⠀

჻ The Number added to both is 20.

Answer 2

Answer:

20

=> The ratio of two natural numbers is 5:6 , if a numbers is added to both numbers , the ratio becomes 7:8 if the larger exceeds the smaller number by 10 then the number added is 20 .

Please kindly refer to the given Attachment above.

$\bold{\boxed{ \huge{ \boxed{ \orange{ \small{ \boxed{ \huge{ \red{ \bold{ \: Thanks}}}}}}}}}} \:$