Question

The average of six numbers is 30, if the average of first four is 25 and that of last three is 30, the fourth number is ?

• A. 35
• B. 10
• C. 25
• D. 40

Answer 1

Answer: (B)

10

$\Rightarrow$ Let the sex numbers be $x_1,x_2,x_3,x_4,x_5,x_6$

$\Rightarrow$ Average of six number is $30$

$\therefore$ $\frac{x_1+x_2+x_3+x_4+x_5+x_6}{6}=30$

$\therefore$ $x_1+x_2+x_3+x_4+x_5+x_6=180$ -------- ( 1 )

$\Rightarrow$ Average of first four number is $25$

$\therefore$ $\frac{x_1+x_2+x_3+x_4}{4}=25$

$\therefore$ $x_1+x_2+x_3+x_4=100$ ---------- ( 2 )

Subtracting ( 2 ) from ( 1 ) we get,

$x_5+x_6=80$ -------- ( 3 )

$\Rightarrow$ Average of last three numbers is $30$

$\therefore$ $\frac{x_4+x_5+x_6}{3}=30$

$\therefore$ $x_4+x_5+x_6=90$ ------- ( 4 )

Now, subtracting ( 3 ) from ( 1 ) we get,

$x_4=10$

$\therefore$ The fourth number is $10$.