Question

The present age of Sourav and Gourav are in the ratio 4:5. 8 years from now the ratio of their ages be 5:6. Then their ages are in years.​

Answer 1

Answer:

Let ages of them be x

According to question,

4x+8+5x+8=5x+6x

9x+16=11x

11x–9x=16

2x=16

x=16/2

x=8

Therefore,

Present age of anu=4x

4x8

32 years

Present age of raj=5x

5x8

40years

Step-by-step explanation:

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Answer 2

$\overline{\underline{\boxed{\sf GIVEN \darr}}}$

The present age of Sourav and Gourav are in the ratio 4:5. 8 years from now the ratio of their ages be 5:6. Then their ages are in years.

$\overline{\underline{\boxed{\sf SOLUTION \darr}}}$

Given that :

Age

Sourav : Gourav = 4 : 5

So,

Sourav's ratio of age = 4

Gourav's ratio of age = 5

Let the constant multiple be x

Therefore,

Sourav's age = 4x

Gourav's age = 5x

After 8 years,

Sourav's age becomes = 4x + 8

Gourav's age becomes = 5x + 8

Henceforth the result of their ages after 8 years is : 5 : 6

So, the equation is :

$✏ \: { \sf \purple{\frac{4x + 8}{5x + 8} = \frac{5}{6} }}$

By cross multiplying we get

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

$✏ \: \green{ \sf24x + 48 = 25x + 40}$

Transposing them we get

$✏ \: \pink{ \sf25x - 24x = 48 - 40}$

$✏ \: \underline{ \boxed{\blue{ \sf x = 8}}}$

Now, their respective ages in years are :

Sourav's age = 4x

⟼ 4 × 8

⟼ 24

Hence, Sourav's age is 24 years

Gourav's age = 5x

⟹ 5 × 8

⟹ 40

Hence, Gourav's age is 40 years