Question

16. The present ages of Arman's parents are in the ratio 4 : 5 Eight years later, the ratio of their
ages will change to 5:6. Find their present ages.​

Answer 1

Answer:

The present age of 1 st parent is 32 years

The present age of 2 nd parent is 40 years

Step-by-step explanation:

Let,

The present age of 1 st parent = 4x

The present age of 2nd parent = 5x

Eight years later,

The age of 1 st parent = 4x + 8

The age of 2nd parent = 5x + 8

And their age ratio will be = 5 : 6

So,

⇒ $\frac{4x + 8}{5x + 8} \: \: = \frac{5}{6}$

⇒ 6 ( 4x + 8) = 5 ( 5x + 8)

⇒ 24x + 48 = 25x + 40

⇒ 24x - 25x = 40 - 48

⇒ - 1x = - 8

⇒ 1x = 8

⇒ x = 8

★ Value of 4x:

⇒ 4 (8)

⇒ 4 × 8

⇒ 32

★ Value of 5x

⇒ 5 (8)

⇒ 5 × 8

⇒ 40

Therefore,

The present age of 1 st parent is 32 years

The present age of 2 nd parent is 40 years

Answer 2

Step-by-step explanation:

$\sf \red {\underline{\underline{Given:-}}}$

• The present ages of Arman's parents are in the ratio 4:5

• Eight years later ratio of their ages changes to 5:6

$\sf \blue {\underline{\underline{To\:Find:-}}}$

• The present ages of Arman's ages

$\sf \green {\underline{\underline{Solution:-}}}$

Let the present ages of Arman's parents be 4x and 5x

Eight years later:-

Age of 1st parent = 4x + 8

Age of 2nd parent = 5x + 8

Given, the ratio changes to 5 : 6

So:-

$\sf{ \implies(4x + 8) \: :(5x + 8) = 5 \: : 6}$

$\sf{ \implies \dfrac{ (4x + 8)}{(5x + 8)} }= \dfrac{5}{6}$

By cross multiplication :-

$\sf{ \implies { 6(4x + 8)} = {5(5x + 8)} }$

$\sf{ \implies { 24x + 48} = {25x + 40} }$

$\sf{ \implies { 25x + 24x} = {48 - 40} }$

$\sf{ \implies { x} = {8} }$

Age of first parent = 4x = 4× 8 = 32

Age of second parent = 5x = 5 × 8 = 40

Hence;

$\boxed{ \sf \pink {Present \: age \: of \: the \: first \: parent \: \: = 32\:years}}$

$\boxed{ \sf \purple{Present \: age \: of \: second \: parent \: \: = 40 \: years}}$