Question

The ratio of teenagers to adults in a town is 30:1. if the teenagers are increased by fifty and the adults by five, the ratio will change to 25:1.how many adults are present in the town at present ?

Answer 1

$\text{Let the number of teenagers in town be x and the number of adults in the town be y} \\ \\ \text{The original ratio between the teenagers and adults} = 30:1 \\ \implies \frac{x}{y} = \frac{30}{1} \\ \implies x = 30y ~ ~.......1 \\ \\ \text{now if the number of teenagers is increased by 50 and number of adults is increased by 5 the new ratio is} = 25 : 1\\ \implies \frac{x+50}{y+5} = \frac{25}{1}\\ \implies x+50 = 25y + 125 \\ \implies 30y + 50 = 25y + 125~(\text{putting value of x from equation 1} ) \\ \implies 30y-25y = 125-50\\ \implies 5y = 75\\ \implies y = \frac{75}{5} \\ \implies y = 15 \\ \text{Hence number of adults in the town at present is} 15 \\ \text{Number of teenagers in present} = 15\times30=450 \:$