Question

The average age of A and B 3 years ago was 18 years. The average age with C is 22 years, so C is the age​

Answer 1

Given :

• The average age of A and B 3 years ago was 18 years.
• The average age with C is 22 years.

To find :

• Current age of C =?

Step-by-step explanation :

Let age of A be a.

Let age of B be b.

Let age of C be c.

Three years ago the age of a and b was 18 years. (GIVEN)

The average age of c = 22 years

➠ Now, we will have to find the age of C, to find the age of c, we will apply the following steps :

⟹ (a-3) + (b-3) / 2 = 18

⟹ a + b - 6 = 18 × 2

⟹ a + b - 6 = 36

⟹ a + b = 36 + 8

⟹ a + b = 42

Now, Therefore here we got the age of a + b as 42

So, now we will find the age of C, using the given age of a + b

⟹ a + b + c / 3 = 22

⟹ 42 + c / 3 = 22

⟹ 42 + c = 22 × 3

⟹ 42 + c = 66

⟹ c = 66-42 = 24

Hence, the current age of c is 24 years.

Answer 2

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$\huge{\underline {\underline{{\purple{ \sf Solution} }}}}$

$\green{ \bold{Let \: the \: present \: age \: of \: A, B,C \: be \: a, b, c \: respectively}}$

$\orange{ \rm \therefore 3 \: years \: ago \: the \: ages \: were}$

$\gray{ : \implies \tt{ \dfrac{(a - 3) + (b - 3)}{2} = 18 }}$

$\pink{ \tt : \implies \dfrac{a + b - 6}{2} = 18}$

$\pink{ \tt : \implies a + b - 6 = 18 \times 2 }$

$\pink{ \tt : \implies a + b - 6 = 36 }$

$\pink{ \tt : \implies a + b = 36 + 6}$

$\pink{ \tt : \implies a + b = 42 }$

$\purple{ \therefore \rm Value \: of \: a + b = 42}$

$\green{ \sf Now, According \: to \: Question}$

$\pink{ \sf \longrightarrow \dfrac{a + b + c}{3} = 22}$

$\pink{ \sf \longrightarrow \dfrac{42 + c}{3} = 22}$

$\pink{ \sf \longrightarrow 42 + c = 22 \times 3}$

$\pink{ \sf \longrightarrow 42 + c = 66}$

$\pink{ \sf \longrightarrow c = 66 - 42}$

$\pink{ \sf \longrightarrow c = 24}$

${\green{ \underbrace{\boxed{\underline{\underline{\purple{ \tt 24 \: is \: the \: Present \: age \: of \: C }}}}}}}$

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