UKMT Pink Kangaroo, 2018

Number theory Difficulty 2.0 Junior Find the answer United Kingdom

Some of the digits in the following correct addition have been replaced by the letters $P$ , $Q$ , $R$ and $S$ , as shown:

$\begin{array}{r} P\,4\,5 \\ +\,Q\,R\,S \\ \hline 6\,5\,4 \end{array}$

What is the value of $P+Q+R+S$ ?

(A) $14$ (B) $15$ (C) $16$ (D) $17$ (E) $24$

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