MCQ
$0.\overline{68}+0.\overline{73}=?$
- A$1.\overline{41}$
- ✓$1.\overline{42}$
- C$0.\overline{141}$
- DNone of these.
✓
Answer
Correct option: B.
$1.\overline{42}$
Consider, $\text{x}=0.\overline{68}$
$\Rightarrow\text{x}=0.6868\dots \dots(\text{i})$
Multiply by $100$
$\Rightarrow\text{100x}=68.68\dots \dots(\text{ii})$
Subtracting $(i)$ from $(ii),$ we get
$\text{99x}=68$
$\Rightarrow\text{x}=\frac{68}{99}\dots(\text{A})$
Consider, $\text{x}=0.\overline{73}$
$\Rightarrow x = 0.7373 ...... (iii)$
Multiply by $100$
$\Rightarrow 100x = 73.73 ...... (iv)$
Subtracting $(iii)$ from $(iv),$ we get
$\text{99x}=73$
$\Rightarrow\text{x}=\frac{73}{99}\dots(\text{B})$
Adding $(A)$ and $(B),$ gives us
$\frac{68}{99}+\frac{73}{99}=\frac{141}{99}=1.42424\dots$
$\Rightarrow0.\overline{68}+0.\overline{73}=1.42424\dots$
$=1.\overline{42}$
$\Rightarrow\text{x}=0.6868\dots \dots(\text{i})$
Multiply by $100$
$\Rightarrow\text{100x}=68.68\dots \dots(\text{ii})$
Subtracting $(i)$ from $(ii),$ we get
$\text{99x}=68$
$\Rightarrow\text{x}=\frac{68}{99}\dots(\text{A})$
Consider, $\text{x}=0.\overline{73}$
$\Rightarrow x = 0.7373 ...... (iii)$
Multiply by $100$
$\Rightarrow 100x = 73.73 ...... (iv)$
Subtracting $(iii)$ from $(iv),$ we get
$\text{99x}=73$
$\Rightarrow\text{x}=\frac{73}{99}\dots(\text{B})$
Adding $(A)$ and $(B),$ gives us
$\frac{68}{99}+\frac{73}{99}=\frac{141}{99}=1.42424\dots$
$\Rightarrow0.\overline{68}+0.\overline{73}=1.42424\dots$
$=1.\overline{42}$
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