Question

Three consecutive whole numbers are such that if they be divided by 5, 3 and 4 respectively; the sum of the quotients is 40. Find the numbers.

Answer 1

Let the three consecutive whole numbers be x, x+1 and x+2

According to the statement :

$\frac{x}{5}+\frac{x+1}{3}+\frac{x+2}{4}=40\Rightarrow \frac{x}{5}\times 60+\frac{x+1}{3}\times 60+\frac{x+2}{4}\times 60=40\times 60$

[Multiplying each term by 60 because L.C.M. of denominators = 60]

$\Rightarrow 12x+20(x+1)+15(x+2)=2400\Rightarrow 12x+20x+20+15x+30=2400\Rightarrow 12x+20x+15x=2400-20-30\Rightarrow 47x=2350\Rightarrow x=\frac{2350}{47}\Rightarrow x=50\therefore x+1=50+1=51x+2=50+2=52$

$\therefore$ Three consecutive whole numbers are 50, 51 and 52