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A sum of money is sufficient to pay A's wages for 21 days and B's wages for 28 days. The same money is sufficient to pay the wages of both for ?

A sum of money is sufficient to pay A's wages for 21 days and B's wages for 28 days. The same money is sufficient to pay the wages of both for ? Correct Answer 12 days

$$\eqalign{ & {\text{Let total money be Rs}}{\text{.}}x \cr & {\text{A's 1day's wages}} = {\text{Rs}}{\text{.}}\frac{x}{{21}} \cr & {\text{B's 1day's wages}} = {\text{Rs}}{\text{.}}\frac{x}{{28}} \cr & \therefore \left( {{\text{A}} + {\text{B}}} \right){\text{'s 1 day's wages}} \cr & = {\text{Rs}}{\text{.}}\left( {\frac{x}{{21}} + \frac{x}{{28}}} \right) \cr & = {\text{Rs}}{\text{.}}\frac{x}{{12}} \cr} $$
∴ Money is sufficient to pay the wages of both for 12 days.

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