Question

Four numbers are in AP whose sum is 50 and the greatest number is four times the smallest number. Find the greatest number among the four.

• A. 23
• B. 26
• C. 20
• D. 29

Answer 1

The correct option is C

20

Let four numbers in A.P. be $a-3d,a-d,a+danda+3d$ respectively.
Then, $a-3d+a-d+a+d+a+3d=50$
$\Rightarrow 4a=50\Rightarrow a=\frac{25}{2}$
Also given that the greatest number is four times the smallest number.
Hence $a+3d=4(a-3d)\Rightarrow a+3d=4(a-3d)\Rightarrow a+3d=4a-12d\Rightarrow 15d=3a\Rightarrow a=5d\Rightarrow \frac{25}{2}=5d\Rightarrow d=\frac{5}{2}$
$\therefore$ The numbers are
$(\frac{25}{2}-\frac{3\times 5}{2}),(\frac{25}{2}-\frac{5}{2}),(\frac{25}{2}+\frac{5}{2})and(\frac{25}{2}+\frac{3\times 5}{2}$),
i.e. ($\frac{25}{2}-\frac{15}{2}),(\frac{20}{2}),(\frac{30}{2}\left)and\right(\frac{40}{2})$
i.e. 5, 10, 15 and 20