Question
Find three smallest consecutive natural numbers such that the difference between one-third of the largest and one-fifth of the smallest is at least 3
✓
Answer
Let first least natural number $=x$
then second number $=x+1$
and third number $=x+2$
According to the condition $\frac{1}{3}(x+2)-\frac{1}{5}(x) \geq 3$
$5 x+10-3 x \geq 45$...(Multiplying by 15 the L.C.M. of 3 and 5 )
$2 x \geq 45-10 \Rightarrow 2 x \geq 35$
$
x \geq \frac{35}{12} \Rightarrow x \geq 17 \frac{1}{2}
$
$\because x$ is a natural least number
$
\therefore x =18
$
$\therefore$ First least natural number $=18$
Second number $=18+1=19$
and third number $h=18+2=20$
Hence least natural numbers are $18,19,20$.
then second number $=x+1$
and third number $=x+2$
According to the condition $\frac{1}{3}(x+2)-\frac{1}{5}(x) \geq 3$
$5 x+10-3 x \geq 45$...(Multiplying by 15 the L.C.M. of 3 and 5 )
$2 x \geq 45-10 \Rightarrow 2 x \geq 35$
$
x \geq \frac{35}{12} \Rightarrow x \geq 17 \frac{1}{2}
$
$\because x$ is a natural least number
$
\therefore x =18
$
$\therefore$ First least natural number $=18$
Second number $=18+1=19$
and third number $h=18+2=20$
Hence least natural numbers are $18,19,20$.
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