Question

Three years ago the average age of A and B was 18 years. With C joining them, the average age becomes 22 years. How old is C now?​

Answer 1

Answer:

C is 24 years old.

Step-by-step explanation:

$\bold{\underline{\underline{Assume\::}}}$

Let the -

• Present age of A = x years
• Present age of B = y years
• Present age of C = z years

$\bold{\underline {\underline {Solution \::}}}$

Three years ago the average age of A and B was 18 years.

Now,

• Age of A = (x - 3) years
• Age of B = (y - 3) years

According to question

⇒ $\dfrac{(x-3)\:+\:(y-3)}{2}\:=\:18$

Cross-multiply them

⇒ $(x-3)\:+\:(y-3)\:=\:36$

⇒ $x\:-\:3\:+\:y\:-\:3\:=\:36$

⇒ $x\:+\:y\:=\:36\:+\:6$

⇒ $x\:+\:y\:=\:42$ ___ (eq 1)

The average of A, B and C is 22 years.

⇒ $\dfrac{(x)\:+\:(y)\:+\:(z)}{3}\:=\:22$ ___ (eq 2)

Cross-multiply them

⇒ $x\:+\:y\:+\:z\:=\:66$

⇒ $42\:+\:z\:=\:66$

⇒ $z\:=\:66\:-\:42$

[From (eq 1)]

⇒ $z\:=\:24$

∴ Present age of C is 24 years.

_______________________________

Verification

From above calculations we have z = 24.

Put value of z in (eq 2)

→ $\frac{x\:+\:y\:+\:z}{3}\:=\:22$

→ $\frac{42\:+\:24}{3}\:=\:22$

→ $\frac{66}{3}\:=\:22$

→ $22\:=\:22$

Answer 2

${\bold{\underline{\underline{Answer:}}}}$

${\bold{\therefore Age\:of\:C=24\:years}}$

${\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

• In the given question information given about three years ago the average age of A and B was 18 years. With C joining them, the average age becomes 22 years.

• We have to find how old is C now?

$\underline \bold{Given : } \\ \implies Avg .\: age \: of \: A \: and \: B= 18 \: years \\ \\ \implies Avg. \: age \: of \: A,\: B \: and \: C= 22 \\ \\ \underline \bold{To \: Find : } \\ \implies Age \: of \: C= ?$

• According to given question :

$\bold{ For \: average \: of \: A \: and \: B} \\ \implies \frac{(A - 3) + (B- 3)}{2} = 18 \\ \\ \implies A - 3+ B - 3= 18 \times 2 \\ \\ \implies A+ B= 36 + 6 \\ \\ \implies A + B = 42- - - - - (1) \\ \\ \bold{for \: Avg \: of \: A , \: B\: and \: C : } \\ \implies\frac{A+ B + C}{3} = 22 \\ \\ \implies A + B + C = 22 \times 3 \\ \\ \implies A+ B + C= 66 - - - - - (2) \\ \\ \bold{Subtracting \: (2) \: from \: (1)} \\ \implies A + B- (A+ B+ C) = 42 - 66 \\ \\ \implies \cancel A + \cancel B - \cancel A- \cancel B - C= - 24 \\ \\ \implies \cancel - C = \cancel - 24\\ \\ \bold{\implies C = 24 \: years} \\ \\ \bold{\therefore Age \: of \: C\: is \: 24 \: years}$