If one quarter of the sum of two numbers is 14 and half of their difference is 5, then the numbers are
If one quarter of the sum of two numbers is 14 and half of their difference is 5, then the numbers are..
A) 23, 30
B) 33, 45
C) 23, 33
D) 25, 35
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Correct option is (C) 23, 33
Let the numbers are a and b.
\(\therefore\) Their sum = a+b
and their difference = a - b
Then according to given conditions, we have
\(\frac14(a+b)=14\)
\(\Rightarrow\) a+b = 56 ____________(1)
And \(\frac12(a-b)=5\)
\(\Rightarrow\) a - b = 10 ____________(2)
By adding equations (1) & (2), we get
(a + b) + (a - b) = 56+10
\(\Rightarrow\) 2a = 66
\(\Rightarrow\) a = 33
\(\therefore\) b = 56 - a (From (1))
= 56 - 33 = 23
Hence, the numbers are 33 and 23.
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