The ratio of present ages of mother and son is 6:1 after 10 years the

1.	The ratio of present ages of mother and son is 6:1 after 10 years the ratioof their ages will be 8: 3. find the presentages of mother and son.years the ratio
Answer» Given: • The ratio of present ages of MOTHER and son is 6:1. • After 10 years the ratio of their ages will be 8:3. To calculate: • The present ages of mother and son. Calculation: Here, we'll ASSUME their ages as 6x and 1x respectively, 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. As, the ratio of present ages of mother and son is 6:1 so, let Present age of mother = 6x Present age of son = 1x After ten years, Age of mother = 6x + 10 Age of son = 1x + 10 According to the question, $\longrightarrow \sf{ \dfrac{6x+10}{1x+10} = \dfrac{8}{3} }$ By cross multiplication, $\longrightarrow \sf{3(6x+10) = 8(1x+10) }$ By distributive property, $\longrightarrow \sf{3(6x) +3(10) = 8(1x)+8(10) }$ Performing multiplication. $\longrightarrow \sf{18x+30 = 8x+80}$ Transposing like terms. $\longrightarrow \sf{18x-8x = 80-30}$ $\longrightarrow \sf{10x= 50}$ $\longrightarrow \sf{x= \dfrac{50}{10}}$ $\longrightarrow\boxed{ \sf{x= 5}}$ So, → Present age of mother = 6x years → Present age of mother = 6(5) years → Present age of mother = 30 years And, → Present age of son = 1x years → Present age of son = 1(5) years → Present age of son = 5 years. Therefore,the present ages of mother and son are 30 years and 5 years.

The ratio of present ages of mother and son is 6:1 after 10 years the ratioof their ages will be 8: 3. find the presentages of mother and son.years the ratio

Answer»

Given:

• The ratio of present ages of MOTHER and son is 6:1.

• After 10 years the ratio of their ages will be 8:3.

To calculate:

• The present ages of mother and son.

Calculation:

Here, we'll ASSUME their ages as 6x and 1x respectively, 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.

As, the ratio of present ages of mother and son is 6:1 so, let

Present age of mother = 6x
Present age of son = 1x

After ten years,

Age of mother = 6x + 10
Age of son = 1x + 10

According to the question,

$\longrightarrow \sf{ \dfrac{6x+10}{1x+10} = \dfrac{8}{3} }$

By cross multiplication,

$\longrightarrow \sf{3(6x+10) = 8(1x+10) }$

By distributive property,

$\longrightarrow \sf{3(6x) +3(10) = 8(1x)+8(10) }$

Performing multiplication.

$\longrightarrow \sf{18x+30 = 8x+80}$

Transposing like terms.

$\longrightarrow \sf{18x-8x = 80-30}$

$\longrightarrow \sf{10x= 50}$

$\longrightarrow \sf{x= \dfrac{50}{10}}$

$\longrightarrow\boxed{ \sf{x= 5}}$

So,

→ Present age of mother = 6x years

→ Present age of mother = 6(5) years

→ Present age of mother = 30 years

And,

→ Present age of son = 1x years

→ Present age of son = 1(5) years

→ Present age of son = 5 years.

Therefore,the present ages of mother and son are 30 years and 5 years.