Question

One quarter of the sum of two numbers is $14$ and half their difference is $5$. The numbers are

• A. $23,30$
• B. $33,43$
• C. $23,33$
• D. $25,35$

Answer 1

Answer: (C)

$23,33$

Let the first number be x and the second number be y. Then
$\frac{1}{4}(x+y)=14$
$\therefore x+y=14\times 4$ .....(1)
or $\frac{1}{2}(x-y)=5$
$\therefore x-y=10$ ..............(2)
Adding (1) and (2), we get
$x+y=56$
$\underset{–}{x-y=10}$
$2x=66$
or $x=33$
$\therefore 33-y=10$
or $33-10=y$
or $23=y$