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Answer :
Let the number be x.
Condition I: x – \(\frac { 5 }{ 2 }\)
Condition II: 8 × (x – \(\frac { 5 }{ 2 }\))
Condition III: 8 × (x – \(\frac { 5 }{ 2 }\)) = 3x
\(\Rightarrow\) 8x – \(\frac { 5 }{ 2 }\) × 8 = 3x [Solving the bracket]
\(\Rightarrow\)8x – 20 = 3x
\(\Rightarrow\) 8x – 3x = 20 [Transposing 3x to LHS and 20 to RHS]
\(\Rightarrow\) 5x = 20
\(\Rightarrow\) x = 20 ÷ 5 = 4 [Transposing 5 to RHS]
Hence, x = 4 is the required number.