# A x 4 = E B Ã· 4 = E C + 4 = E D - 4 = E ___________ & A + B + C + D = 100 *what is the value of E ?*

$\begin{array}{l}\text{Given :}\ A\times4=EB\div4=EC+4=ED-4=E\\ A,\ B,\ C,\ D\ \text{ w.r.t.}\ E\ \ \text{are}:\\ A=\frac{E}{4}\\ B=4E\\ C=E-4\\ D=E+4\\ \text{Also,}\\ A+B+C+D=100\\ \text{Hence,}\\ \Rightarrow\frac{E}{4}+4E+(E-4)+(E+4)=100\\ \Rightarrow\frac{E}{4}+4E+E-4+E+4=100\\ \Rightarrow\frac{E}{4}+4E+2E=100\\ \Rightarrow\frac{E}{4}+6E=100\\ \Rightarrow E+24E=4*100\\ \Rightarrow25E=400\\ \Rightarrow E=\frac{400}{25}\\ \Rightarrow E=16\\ \\ \end{array}$

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