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# The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is:

Option :

Explanation:

Solution:
$\begin{array}{rl}& \text{Let}\phantom{\rule{thinmathspace}{0ex}}\text{the}\phantom{\rule{thinmathspace}{0ex}}\text{number}\phantom{\rule{thinmathspace}{0ex}}\text{be}\phantom{\rule{thinmathspace}{0ex}}x\phantom{\rule{thinmathspace}{0ex}}\text{and}\phantom{\rule{thinmathspace}{0ex}}y\\ & \text{Then},\phantom{\rule{thinmathspace}{0ex}}xy=9375\phantom{\rule{thinmathspace}{0ex}}\text{and}\phantom{\rule{thinmathspace}{0ex}}\frac{x}{y}=15\\ & \frac{xy}{\left(x/y\right)}=\frac{9375}{15}\\ & ⇒{y}^{2}=625\\ & ⇒y=25\\ & ⇒x=15y=\left(15×25\right)=375\\ & \therefore \text{Sum}\phantom{\rule{thinmathspace}{0ex}}\text{of}\phantom{\rule{thinmathspace}{0ex}}\text{the}\phantom{\rule{thinmathspace}{0ex}}\text{number}\\ & =x+y=375+25=400\end{array}$