An electorate

In an electorate, 3/4 th of the voters are Tamils. Of the remaining 2/3 rd are Muslims, and the others are Sinhalese. If the number of Sinhalese in that electorate is 587, find the number of voters in that electorate.

Correct answer:

x =  7044

Step-by-step explanation:

$$\begin{gathered} S=587 \\ {r}_1=\frac{3}{4}=0.75 \\ {r}_2=\frac{2}{3}\cdot \frac{1}{4}=\frac{2\cdot 1}{3\cdot 4}=\frac{2}{12}=\frac{1}{6}\doteq 0.1667 \\ {r}_3=1-r_1-r_2=1-\frac{3}{4}-\frac{1}{6}=\frac{1}{12}\doteq 0.0833 \\ {r}_3\cdot x=S \\ x=S/r_3=587/\frac{1}{12}=587:\frac{1}{12}=587\cdot \frac{12}{1}=\frac{587\cdot 12}{1}=\frac{7044}{1}=7044 \\ \text{ Verifying Solution: } \\ T=r_1\cdot x=0.75\cdot 7044=5283 \\ M=r_2\cdot x=0.1667\cdot 7044=1174 \\ {S}_2=r_3\cdot x=0.0833\cdot 7044=587 \end{gathered}$$

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