question_answer 10)

                The ages of Rahul and Haroon are in the ratio 5 : 7. Four years later the sum of their ages will be 56 years What are their present ages?

Answer:

                Let the present ages of Rahul and Haroon be \[5x\] years and \[7x\] years respectively. Four years later Age of Rahul \[=(5x+4)\] years Age of Haroon \[=(7x+4)\] years \[\because \]     Four years later the sum of their ages will be 56 years. \[\therefore \]  \[(5x+4)\,+(7x+4)=56\] \[\Rightarrow \]               \[12x+8=56\] \[\Rightarrow \]               \[12x=56-8\]                      | Transposing 8 to RHS \[\Rightarrow \]               \[12x=48\] \[\Rightarrow \]               \[x=\frac{48}{12}=4\]                     | Dividing both sides by 12 \[\Rightarrow \]               \[5x=5\times 4=20\] and        \[7x=7\times 4=28\] Hence, their present ages are 20 years and 28 years. Check: \[20:28=\frac{20}{28}\,=\frac{20\div 4}{28\div 4}=\frac{5}{7}\] \[=5:7\]                                                | as desired \[20+4=24\] \[28+4=32\] \[24+32=56\].