Question

Rita is 6 years older than her younger sister after 10 years, the sum of their ages will be 50 years.find their present ages

Answer 1

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✺Answer:

♦️GiveN

• Presently, Rita is 6 years older than her younger sister.
• After 10 years, sum of their ages will be 50.

♦️To FinD

• Their present ages.....?

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✺Explanation of Q.

This question asking about the present ages of Rita and Her younger sister. It also have two conditions ,so that we could solve this but this question can be solved in two ways.

• By using two variables.
• By using one variable.

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✺Solution

$\Large{\rm{\underline{\underline{\purple{Method-1}}}}}$

By using 1 variable ,

Let the present age of Younger sister be x

Then, the present age of Rita is x + 6

Age of sister after 10 years = x + 10

Age of Rita after 10 years = x +16

It given that after 10 years, The sum.of their ages is 50

So by solving this equation,

$\large{ \rm{ \rightarrow \: x + 10 + x + 16 = 50}} \\ \\ \large{ \rm{ \rightarrow \: 2x + 26 = 50}} \\ \\ \large{ \rm{ \rightarrow \: 2x = 24}} \\ \\ \large{ \rm{ \rightarrow \: x = 12}}$

$\large{ \rm{ \pink{ \therefore{age \: of \: younger \: sister = 12 \: years}}}} \\ \\ \large{ \rm{ \green{ \therefore{age \: of \: rita = \: x + 6 = 18 \: years}}}}$

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$\Large{ \rm{ \underline{ \underline{ \purple{Method - 2}}}}}$

By using 2 variables,

Let the age of rita be x and age of her sister be y.

Then we have rita's age x ,6 more than the sister's age So, Equation would be

$\large{ \rm{ \rightarrow \: x = y + 6}}\\ \\ \large{\rm{\rightarrow \: x-y=6}}......(1)$

After ten 10 years, Rita's age = x + 10

Younger sister's age = y + 10

Together their ages add upto 50

Then equation would be,

$\large{ \rm{ \rightarrow \: x + 10 + y + 10 = 50}} \\ \\ \large{ \rm{ \rightarrow \: x + y + 20 = 50}} \\ \\ \large{ \rm{ \rightarrow \: x + y = 30}}........(2)$

So, by adding equation (1) and equation (2)

$\large{ \rm{ \rightarrow \: x + y + x - y = 36}} \\ \\ \large{ \rm{ \rightarrow \: 2x = 36}} \\ \\ \large{ \rm{ \rightarrow \: x = 18}}$

By putting this value in equation (1)

$\large{ \rm{ \rightarrow \:18 - y = 6}} \\ \\ \large{ \rm{ \rightarrow \: y = 12}}$

$\large{ \rm{ \pink{ \therefore \: present \: age \: of \: younger \: sister= 12 \: years}}} \\ \\ \large{ \rm{ \green{ \therefore \: present \: age \: of \: rita = 18 \: years}}}$

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Answer 2

☆ ANSWER:-

▪︎ Given:-

• Rita is 6 years oplder than her younger sister.

• After 10 years thesum of their ages will be 50.

▪︎ To Find:-

• Their present ages.

$\rule{400}4$

▪︎ Now,

• Let us firstly assume the age of Rita's younger sister be x.

• So the age of Rita would be (x+6).

• 10 years after Younger sister's age will be (x+10).

• 10 years after Rita's age will be (x+6+10) = (x+16).

$\rule{400}2$

▪︎ So ATQ:-

$\tt\mapsto(x + 10) + (x + 16) = 50 \: years. \\ \\ \tt\mapsto \: x + 10 + x + 16 = 50 \: years. \\ \\ \tt\mapsto \: x + x + 10 + 16 = 50 \: years. \\ \\ \tt\mapsto2x + 16 = 50 \: years.\\ \\ \tt\mapsto2x = (50 - 26)years. \\ \\ \tt\mapsto2x = 24 \: years. \\ \\ \tt\mapsto \: x = \frac{24 \: years}{2} \\ \\ \tt\large\pink{\fbox {\mapsto\: x = 12years.}}$

$\rule{400}2$

♧ Therefore,

• Rita's present age = (x+6) years. = (12+6) years = 18 years.

• Her younger sister's age = 12 years.

♧ Thus,

${\small{\green{\boxed{\bold{Rita's\:age\:=\:18\:Years.}}}}}$

${\small{\green{\boxed{\bold{\therefore {Younger\:Sister's\:age\:=\:12\:Years.}}}}}}$

$\rule{400}4$