Question

The product of four consecutive natural numbers which are multiples of five is $15000$. Find those natural numbers.

Answer 1

The four consecutive natural numbers which are multiple of five can be written as $5x-5,5x,5x+5,5x+10$
where $x$ is integer
According to question $(5x-5)\times 5x\times (5x+5)\times (5x+10)=15,000$
$\Rightarrow 5^4(x-1)x(x+1)(x+2)=15000$
$\Rightarrow (x-1)x(x+1)(x+2)=\frac{15000}{625}$
$\Rightarrow (x-1)x(x+1)(x+2)=24$
Solve the equation
$x=2$
$\therefore$ Number's are
$5x-5=5\times 2-5=5$
$5x=5\times 2=10$
$5x+5=5\times 2+5=15$
$5x+10=5\times 2+10=20$
$\therefore$ Natural number's are $5,10,15,20$