Find a number whose double is 45 greater than its half. - Vidyadip

Question

Find a number whose double is $45$ greater than its half.

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Answer

Let the requierd number $= x$
Then Four-fifth of the number $= 2x$ And half of it $=\frac{\text{x}}{2}$
$\therefore$ According to the condition:$2\text{x}-\frac{\text{x}}{2}=45$
$\Rightarrow\frac{4\text{x}-\text{x}}{2}=45$
$\Rightarrow\frac{3}{2}\text{x}=45$
$\Rightarrow\text{x}=\frac{45\times2}{3}=30$
$\therefore$ Required number $= 30$
Check: $2\times30-\frac{1}{2}\times30$ $= 6 - 15 = 45$, which is given
$\therefore$ Our answer is correct.

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