question_answer 6)

                Two numbers are in the ratio 5 : 3. If they differ by 18, what are the numbers?

Answer:

                Let the two numbers be \[5x\] and \[3x\]. \[\because \]     They differ by 18 \[\therefore \]  \[5x-3x=18\] \[\Rightarrow \]               \[2x=18\] \[\Rightarrow \]               \[x=\frac{18}{2}=9\]                       | Dividing both sides by 2 \[\Rightarrow \]               \[5x=5\times 9=45\] and        \[3x=3\times 9=27\] Hence, the desired numbers are 45 and 27.                 Check: \[45:27=\frac{45}{27}=\frac{45\div 9}{27\div 9}\]                 \[=\frac{5}{3}\,=5:3\]                     | as desired                 \[4527=18.\]