Board - 3 parts

A board measures 2 meters. The board was divided in the ratio 2:3:5.
1/5 of the first part is white, 1/3 of the second part is painted red, 3/5 of the third part is painted green. The rest of the board is unpainted.
Answer: whether it is correct or wrong.
Q1. The first painted part is 88 cm.
Q2. The 1st, 2nd, and 3rd parts had the same unpainted piece.
Q3. 40 cm of the first part remained unpainted.

Final Answer:

O₁ =  0
O₂ =  0
O₃ =  0

Step-by-step explanation:

$$\begin{gathered} a+b+c=2\text{m} \\ a:b:c=2:3:5 \\ T=2\text{m} \\ a=\frac{2}{2+3+5}\cdot T=\frac{2}{2+3+5}\cdot 2=\frac{2}{5}=0.4\text{m} \\ b=\frac{3}{2+3+5}\cdot T=\frac{3}{2+3+5}\cdot 2=\frac{3}{5}=0.6\text{m} \\ c=\frac{5}{2+3+5}\cdot T=\frac{5}{2+3+5}\cdot 2=1\text{m} \\ B=\frac{1}{5}\cdot a=\frac{1}{5}\cdot 0.4=\frac{2}{25}=0.08\text{m} \\ C=\frac{1}{3}\cdot b=\frac{1}{3}\cdot 0.6=\frac{1}{5}=0.2\text{m} \\ Z=\frac{3}{5}\cdot c=\frac{3}{5}\cdot 1=\frac{3\cdot 1}{5}=\frac{3}{5}=0.6\text{m} \\ N=T-B-C-Z=2-0.08-0.2-0.6=\frac{28}{25}=1\frac{3}{25}=1.12 \\ B\ne 88cm \\ {O}_1=0 \end{gathered}$$

$$\begin{gathered} n_1=a-B=0.4-0.08=\frac{8}{25}=0.32\text{m} \\ {n}_2=b-C=0.6-0.2=\frac{2}{5}=0.4\text{m} \\ {n}_3=c-Z=1-0.6=\frac{2}{5}=0.4\text{m} \\ {n}_1\ne n_2 \\ {n}_2=n_3 \\ {O}_2=0 \end{gathered}$$

$$\begin{gathered} n_1\ne 40cm \\ {O}_3=0 \end{gathered}$$

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