Question

the sum of ages of A and B is 55 years if the ratio of the ages 6.5 find the ages​

Answer 1

$\underline{ \underline{ \Large \pmb{\sf { \purple{Answer:}} }} }$

• Age of A is 30 years.

• Age of B is 25 years.

$\underline{ \underline{ \Large \pmb{\sf { \purple{Given:}} }} }$

• The sum of ages of A and B is 55 years.

• Their ages are in the ratio 6:5.

$\underline{ \underline{ \Large \pmb{\sf { \purple{To \: calculate:}} }} }$

• Their ages.

$\underline{ \underline{ \Large \pmb{\sf { \purple{Calculation:}} }} }$

Here, we are given that the ages of A and B are in the ratio of 6:5 and the sum of their ages is 55. We have to find out their ages. We'll firs assume their ages as 6x and 5x where x is the constant natural number. Then, by forming an algebraic equation and by solving that equation we'll find the value of x and their ages.

⠀⠀⠀⠀⠀_____________

Let ,

• Age of A = 6x years
• Age of B = 5x years

According to the question,

$\mapsto \sf { Age \: of \: A + Age \: of \: B = 55}$

$\mapsto \sf { 6x + 5x = 55}$

$\mapsto \sf { 11x = 55}$

$\mapsto \sf { x =\cancel{\dfrac{ 55}{11}}}$

$\mapsto \underline { \boxed{\pmb{\rm\red{x = 5}}}}$

Henceforth,

$\longrightarrow \sf {A's \: age = 6x \:years }$

$\longrightarrow \sf {A's \: age = 6(5) \:years }$

$\mapsto \underline { \boxed{\pmb{\rm\purple{ A's \: age = 30 \:years}}}}$

Also,

$\longrightarrow \sf {B's \: age = 5x \:years }$

$\longrightarrow \sf {B's \: age = 5(5) \:years }$

$\mapsto \underline { \boxed{\pmb{\rm\purple{ B's \: age = 25 \:years}}}}$

Therefore,

• Age of A is 30 years.
• Age of B is 25 years.