Question

write answer help me ​

Answer 1

${ \large{ \underline{ \red{ \pmb{ \frak{Given...}}}}}}$

➼ A mother of a son is 20 years older than her son.

➼ After the time period of 4 years the ratio of their ages would be 17 : 27

${ \sf{ \red{ \bigstar \: Hint : }}}$ Consider the age of a son as x

${ \large{ \underline{ \red{ \pmb{ \frak{To\: find...}}}}}}$

➼ What are the ages of the mother and the son?

${ \large{ \underline{ \red{ \pmb{ \frak{Full\:solution...}}}}}}$

➱ Here,

• ↝ Let's consider the age of the son as ${\bf{\pink{x}}}$

• ↝ Let's consider the age of the mother as ${\bf{\pink{x + 20}}}$

${ \cal{ \bold{ \underline{ \bigstar{According \: to \: the \: question : }}}}}$

• ↠ The age of the mother is 20 years more than the child and after four years the ratio of the ages would be

➼ So,

$\longrightarrow \tt \: \frac{x + 4 }{x + 20 + 4 } = \frac{17}{27} \\ \\ \\ \longrightarrow \tt \frac{x + 4}{x + 24} = \frac{17}{27} \: \: \: \: \: \: \: \: \:$

• Cross multiply the fractions now,

↝How do we cross multiply?

★ When To fraction are in the form $\tt \: \dfrac{a}{b} = \dfrac{c}{d}$ we multiply it in the form $\tt \: a \times d = b \times c$

➠ Let's solve the rest now,

$\longrightarrow \tt 27(x + 4) = 17(x + 24) \\ \\ \\ \longrightarrow \tt 27x + 108 = 17x + 408 \\ \\ \\ \longrightarrow \tt 27x - 17x = 408 - 108 \\ \\ \\ \longrightarrow \tt 10x = 300 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt x = \cancel\frac{300}{10} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt \: {\red{{ \underline{ \boxed{ \frak{x = 30}}} \bigstar}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• Henceforth the value of x is 30 years respectively

➱ Now,

• Let's find the ages of the mother and son accordingly

↠ Here,

• Age of the son = 1x = 1(30) = 30 years
• Age of the mother = 30 + 20 = 50 years

${ \large{ \underline{ \red{ \pmb{ \frak{Therefore...}}}}}}$

➼ The ages of the son and mother are ${\red {\sf{30 \: years}}}$ and ${ \red{\sf{50 \: years}}}$ respectively!!

${ \large{ \underline{ \red{ \pmb{ \frak{Verification...}}}}}}$

➼ Let's put the value of 30 instead of x and check weather we went right!

${ : \implies} \rm \frac{x + 4}{x + 20 + 4} = \frac{17}{27} \: \: \\ \\ \\ { : \implies} \rm \frac{30 + 4}{30 + 20 + 4} = \frac{17}{27} \\ \\ \\ { : \implies} \rm \frac{34}{30 + 24} = \frac{17}{27} \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \rm \frac{34}{54} = \frac{17}{27} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \rm 34 \times 2 7= 54 \times 17 \\ \\ \\ { : \implies} \rm { \underline{ \boxed{ \frak{ 918 = 918}}} \star} \: \: \: \: \: \: \: \: \: \: \:$

• L.H.S = R.H.S Hence Verified!!

Answer 2

Given:

• The age of a mother is 20 years more than her son
• After 4 years their ages will be in the ratio of 17 : 27

To Find:

• The present age of the mother and the son

Solution:

• Let's consider the age of the son as x

Now, we know that the age of his mother is 20 years older than him,

➼ So, the age of his mother will be

• X + 20

Now, according to condition one we get,

➱ X + 4 / X + 20 + 4 = 17 / 27

➱ X + 4 / X + 24 = 17/27

➱ 17 ( X + 24 ) = 27( X + 4)

➱ 17x + 408 = 27x + 108

➱ 408 - 108 = 27x - 17x

➱ 10x = 300

➱ x = 30

Hence,

• The ages of the mother and son are 30 and 50 years respectively!!