Question

The ages of A and B are in the ratio 5:2. after 5 years their ages will be in the ratio 15:7. Find their present ages

Answer 1

Answer:

heres your equation

Step-by-step explanation:

$\frac{5x + 5}{2x + 5} = \frac{15}{7}$

Now you can easily solve it

Answer 2

Let 'x' and 'y' be present ages of A and B respectively.

According to first condition;

$\frac{x}{y} = \frac{5}{2} \\ 2x = 5y \\ y = \frac{2}{5} x \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ... \: (i)$

According to second condition;

$\frac{x + 5}{y + 5} = \frac{15}{7} \\ 7x + 35 = 15y + 75 \\ 7x - 15y = 40 \\ 7x - 15( \frac{2}{5}x) = 40 \: \: \: \: \: \: \: \: \: \: \: \: ... \: (from \: i) \\ 7x - 6x = 40 \\ x = 40$

substituting in (i), we get

$y = \frac{2}{5} (40) = 2 \times 8 \\ y = 16$

Hence, present ages of A and B are 40 and 16 respectively.