Question

the ages of Rahul and Lakshmi are in the ratio 5 is to 7 4 years later the sum of their ages will be 56 years what are their present ages

Answer 1

Rahul be x
Laxmi be y
$\frac{x}{y} = \frac{5}{7} \\ 7x - 5y = 0.....1 \\ (x + 4) + (y + 4) = 56 \\ x + y = 48.....2$
multiply 2 with 5
5x+5y=240.....3
adding 1 and 2
$7x - 5y =0 \\ 5x + 5y = 240 \\ 12x = 240 \\ x = 20$
put x=20 in 2
$20 + y = 48 \\ y = 28$
the present ages of Rahul and Laxmi is 20 and 28.
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