Average of two numbers A and B is 20 , that of B and C is 19 and of C and A it is 21 . value of A ?

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The average of two numbers $A$ and $B$ is $20 ,$ that of $B$ and $C$ is $19$ and of $C$ and $A$ it is $21 .$ What is the value of $A ?$

A

$24$

B

$22$

C

$20$

D

$18$

Solution

According to the question,

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

$\Rightarrow A+B=40$ …..$(1)$

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

$\Rightarrow B+C=38$ …..$(2)$

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

$\Rightarrow \quad C+A=42$ …..$(3)$

Adding (1), (2) and (3), we get $\therefore \quad 2 A+2 B+2 C=120$

$\Rightarrow A+B+C=60$ …..$(4)$

$\therefore A=(A+B+C)-(B+C)$

$=60-38=22$

Standard 13

Quantitative Aptitude

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