Problems based on Numbers Test 5

Let the two numbers be x and y.
Ratio of product, sum and difference are 24p : 7p : 1p
According to the statement,
x × y = 24p .......(i)
x + y = 7p .......(i)
x - y = 1p .......(i)
Adding equation (ii) and (iii), we get,
$2\mathit{x}=8\mathit{p}\Rightarrow \mathit{x}=4\mathit{p}$
Put $\mathit{x}=4\mathit{p}$ in equation (ii) we get
$4\mathit{p}+\mathit{y}=7\mathit{p}\Rightarrow \mathit{y}=3\mathit{p}$
Now put the values of x and y in equation (i)
$\mathit{x}\times \mathit{y}=24\mathit{p}$
$4\mathit{p}\times 3\mathit{p}=24\mathit{p}$
$12{\mathit{p}}^2=24\mathit{p}$
$12\mathit{p}=24$
$\mathit{p}=\frac{24}{12}=2$
$\mathit{p}=2$
The product of x and y $=\mathit{x}\times \mathit{y}=4\mathit{p}\times 3\mathit{p}=8\times 6=48.$