Question

The average of A and B is 20, ,
average of B and C is 19 and
average of C and A is 21. Find the value of A.​

Answer 1

Answer:

$\boxed{\bf A = 22}$

Step-by-step explanation:

$\implies \text{average of A and B = 20} \\\\ \frac{A+B}{2}=20 \\\\ A+B=40 \\\\ \implies \text{average of B and C is 19} \\\\ \frac{B+C}{2}=19 \\\\ B+C=38 \\\\ \implies \text{average of C and A is 21} \\\\ \frac{C+A}{2}=21\\\\ C+A=42 \\ ----------- \\ =>A+B=40\\B=40-A \\\\ =>B+C=38\\ 40-A+C=38 \\C-A=38-40\\C-A=-2\\ A-C=2 \\C=A-2\\ \\=>A+C=42 \\ A+A-2=42\\2A-2=42\\2A=42+2\\2A=44\\A=22$

Answer 2

ANSWER :

$\:$

${\bold{\underline{\boxed{A = 22}}}}$

$\:$

EXPLANATION :

$\:$

Formula :

$\:$

$\sf \: AVERAGE = \frac{Sum \: of \: observation}{Number \: of \: observation}$

$\:$

Solution :

$\:$

$\sf \frac{A \: + \: B}{2} = 20$

$\sf \frac{ B \: + \: C}{2} = 19$

$\sf \frac{C \: + \: A}{2} = 21$

$\:$

Now,

$\:$

$\sf \: \frac{a \: + \: b}{2} + \frac{c \: + \: a}{2} - \frac{ b\: + \: c }{2} = 20 + 21 - 19$

Taking LCM 2

↬ $\frac{a \: + \: b \: + \: c \: + \: a \: - \:b \: - \:c }{2} = 41 - 19$

↬ $\frac{2a}{2} = 22$

↬ $a = 22$