Gujarat BoardEnglish MediumSTD 9MathsNumber systems1 Mark
MCQ
The value of $2.\overline{45}+0.\overline{36}$ is:
A
$\frac{67}{33}$
B
$\frac{24}{11}$
C
$\frac{31}{11}$
D
$\frac{167}{110}$
✓
Answer
$\frac{31}{11}$ Solution: Let $\text{x}=2.\overline{45}$ i.e., $\text{x}=2.4545 \ ...(\text{i})$ $\Rightarrow100\text{x}=245.4545 \ ...(\text{ii})$ On subtracting (i) and (ii), we get $99\text{x}=243$ $\Rightarrow\text{x}=\frac{243}{99}$ Let $\text{y}=0.\overline{36}$ i.e., $\text{y}=0.3636 \ ...(\text{iii})$ $\Rightarrow100\text{y}=36.3636 \ ...(\text{iv})$ On subtracting (iii) and (iv), we get $99\text{y}=36$ $\Rightarrow\text{y}=\frac{36}{99}$ $\therefore2.\overline{45}+0.\overline{36}=\text{x}+\text{y}=\frac{\text{243}}{\text{99}}+\frac{\text{36}}{\text{99}}=\frac{\text{279}}{\text{99}}=\frac{\text{31}}{\text{11}}$ Hence, the correct answer is option (c).
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