Question

Find three smallest consecutive whole numbers such that the difference between one-fourth of the largest and one-fifth of the smallest is at least 3

• A. $50,51,52$
• B. $60,61,62$
• C. $51,52,53$
• D. $52,53,54$

Answer 1

The correct option is A $50,51,52$

Let the required whole numbers be x,x+1,x+2
According to the given statement :
$\Rightarrow \frac{x+2}{4}-\frac{x}{5}\ge 3$
$\Rightarrow \frac{5x+10-4x}{20}\ge 3$
$\Rightarrow x+10\ge 60$ i.e. $x\ge 50$
SInce, the smallest value of $x=50$ that satisfies the inequation $x\ge 50$.

Therefore, the smallest consecutive whole numbers are:
$=x,x+1,x+2$
$=50,50+1,50+2$
$=50,51,52$