MathematicsIf (m+n)P2=90 and (m−n)P2=30 , then (m,n) is

If $^{(m + n)} P_{2} = 90$ and $^{(m - n)} P_{2} = 30$ , then $(m, n)$ is

A
$(7, 3)$
B
$(1, 2)$
C
$(9, 1)$
D
$(8, 2)$

Solution:

^{(m + n)} P_{2} = 90 \Rightarrow^{(m + n)} P_{2} =^{10} P_{2} \Rightarrow m + n = 10 \to (1)

$^{(m - n)} P_{2} = 30 \Rightarrow^{(m - n)} P_{2} =^{6} P_{2} \Rightarrow m - n = 6 \to (2)$

On solving equations (1) and (2), we get $m = 8, n = 2$

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