Question

The arithmetic mean of six numbers is $\mathrm{20.5.}$ If two numbers are added to the progression, then the new arithmetic mean is $\mathrm{17.5.}$ If their difference is $3,$ then the two numbers are

• A. $-7$ and $10$
• B. $6$ and $10$
• C. $8$ and $11$
• D. $7$ and $10$

Answer 1

The correct option is D $7$ and $10$

The sum of first six numbers is $6\times 20.5=123.$

Let $x$ and $y(x>y)$ be the two numbers that are added . Then we have
$\frac{123+x+y}{8}=17.5$
$\Rightarrow x+y=17...\left(1\right)$

Another equation is
$x-y=3...\left(2\right)$
Adding the two equations, we get
$x=10$
$\Rightarrow y=7$
So, the numbers are $7$ and $10.$