Question

A number is divided into two parts such that one part is 10 more than the other. If the two parts in the ratio \[5:3\], find the number and the two parts.

Answer 1

Hint: In the given question, take one part of the number as a variable, then the other part will be that variable plus 10. Equate their ratio to \[5:3\]. Then add the two parts to find the number. So, use this concept to reach the solution of the problem.

Complete step-by-step answer:
Let one part of the number is \[x\]
Other part will be variable plus 10 so other part is \[x + 10\]
As the ratio of the two parts is \[5:3\], we have
\[   \Rightarrow \dfrac{{x + 10}}{x} = \dfrac{5}{3} \]
\[   \Rightarrow \left( {x + 10} \right)3 = 5x \]
\[  \Rightarrow 3x + 30 = 5x \]
\[  \Rightarrow 30 = 5x - 3x \]
\[  \Rightarrow 30 = 2x \]
\[  \therefore x = 15 \]
So, one part of the number is 15 and other part is 15 + 10 = 25
Thus, the required number is 15 + 25 = 40.

Note: As the numerator is greater than the denominator in the ratio \[5:3\], we have to take \[x + 10\] in the place of numerator and \[x\] in the place of denominator, since \[x + 10\] is greater than \[x\]. Whenever the number is divided into two parts, we have to add the two parts to obtain the number but not to multiply them.