The difference between two numbers is 16. If one-third of the smaller number is greater than one-seventh of the larger number by 4 then what is the value of greater number?

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Solution

Let the smaller number be $x$ , So larger number = $x + 16$
According to the statement,
$\frac{x}{3} - \frac{(x + 16)}{7} = 4$

$\frac{7 x - 3 x - 48}{21} = 4$
$4 x - 48 = 84$
$4 x = 84 + 48 = 132$
$\Rightarrow x = \frac{132}{4} = 33$
$∴$ The two numbers are $33$ and $(33 + 16)$ i.e. $49$

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The difference between two numbers is 16. If one-third of the smaller number is greater than one-seventh of the larger number by 4 then what is the value of greater number?

Let the smaller number be x, So larger number =x+16According to the statement,x3−(x+16)7=47x−3x−4821=44x−48=844x=84+48=132⇒x=1324=33∴ The two numbers are 33 and (33+16) i.e. 49

Let the smaller number be $x$ , So larger number = $x + 16$
According to the statement,
$\frac{x}{3} - \frac{(x + 16)}{7} = 4$

$\frac{7 x - 3 x - 48}{21} = 4$
$4 x - 48 = 84$
$4 x = 84 + 48 = 132$
$\Rightarrow x = \frac{132}{4} = 33$
$∴$ The two numbers are $33$ and $(33 + 16)$ i.e. $49$