question_answer 11)

                The number of boys and girls in a class are in the ratio 7 : 5. The number of boys is 8 more than the number of girls. What is the total class strength?

Answer:

                Let the number of boys and girls in a class be \[7x\] and \[5x\] respectively. \[\because \]     The number of boys is 8 more than the number of girls. \[\therefore \]  \[7x=5x+8\] \[\Rightarrow \]               \[7x-5x=8\]                         | Transposing \[5x\] to LHS \[\Rightarrow \]               \[2x=8\] \[\Rightarrow \]               \[x=\frac{8}{2}=4\]                          | Dividing both sides by 2 \[\Rightarrow \]               \[7x=7\times 4=28\] and        \[5x=5\times 4=20\] \[\therefore \] Total class strength = Number of boys + Number of girls \[=28+20\] = 48 Hence, the total class strength is 48. Check: \[28:20=\frac{28}{20}=\frac{28\div 4}{20\div 4}\] \[=\frac{7}{5}\,=7:5\]                     |as desired                 \[28=20+8\] Total class strength \[=28+20=48\].