Find the smallest number which when divided by $28$ and $32$ leaves remainders $8$ and $12$ respectively.
Step-by-Step Solution
Key Concept: Notice $28 - 8 = 20$ and $32 - 12 = 20$. Required number is $\text{LCM}(28, 32) - 20$.
$28 - 8 = 20$ and $32 - 12 = 20$. Common difference $= 20$. [0.5 Mark]
$28 = 2^2 \times 7$, $32 = 2^5 \Rightarrow \text{LCM}(28, 32) = 2^5 \times 7 = 32 \times 7 = 224$. [1.0 Mark]
Required number $= 224 - 20 = 204$. [0.5 Mark]
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🎯 Official CBSE Marking Scheme:
Finding common difference $20$: 0.5 Mark
Calculating $\text{LCM}(28, 32) = 224$: 1.0 Mark
Subtracting 20 to get 204: 0.5 Mark
Correct Answer: