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
Let the three consecutive whole numbers be $x, x+1$ and $x+2$
According to the statement:
$\frac{x}{5}+\frac{x+1}{3}+\frac{x+2}{4}=40$
$\Rightarrow \frac{\mathrm{x}}{5} \times 60+\frac{\mathrm{x}+1}{3} \times 60+\frac{\mathrm{x}+2}{4} \times 60=40 \times 60 \ldots [$Multiplying each term by $60$ because $\text{L.C.M}$. of denominators $=60]$
$\Rightarrow 12 x+20(x+1)+15(x+2)=2400$
$\Rightarrow 12 x+20 x+20+15 x+30=2400$
$ \Rightarrow 12 x+20 x+15 x=2400-20-30$
$\Rightarrow 47 x=2350$
$\Rightarrow \mathrm{x}=\frac{2350}{47}$
$x=50$
$x+1=50+1=51$
$x+2=50+2=52$
Three consecutive whole numbers are $50, 51$ and $52$
According to the statement:
$\frac{x}{5}+\frac{x+1}{3}+\frac{x+2}{4}=40$
$\Rightarrow \frac{\mathrm{x}}{5} \times 60+\frac{\mathrm{x}+1}{3} \times 60+\frac{\mathrm{x}+2}{4} \times 60=40 \times 60 \ldots [$Multiplying each term by $60$ because $\text{L.C.M}$. of denominators $=60]$
$\Rightarrow 12 x+20(x+1)+15(x+2)=2400$
$\Rightarrow 12 x+20 x+20+15 x+30=2400$
$ \Rightarrow 12 x+20 x+15 x=2400-20-30$
$\Rightarrow 47 x=2350$
$\Rightarrow \mathrm{x}=\frac{2350}{47}$
$x=50$
$x+1=50+1=51$
$x+2=50+2=52$
Three consecutive whole numbers are $50, 51$ and $52$
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