Question

2 numbers are in the ratio 3:5. if each is increased by 10 the ratio between the new numbers so formed is 5:7. Find the original numbers

Answer 1

the numbers are 3x and 5x
each increased by 10 = 
3x+10 and 5x+10
Ratio of new numbers formed= 5:7= 5/7
So
(3x+10)/(5x+10)= 5/7
Now Cross multiplication
7(3x+10)= 5(5x+10)
21x+70=25x+50
Transposing
70-50=25x-21x
20=4x
x=5

Hope it helps....

Answer 2

Let the numbers be 3x and 5x.

If each increased by 10, the numbers will be 3x+10 and 5x+10
GIven that the ratio of new numbers is 5:7

$\frac{3x+10}{5x+10} = \frac{5}{7} \\ \\ \Rightarrow 7(3x+10) = 5(5x+10)\\ \\ \Rightarrow 21x+70 = 25x+50\\ \\ \Rightarrow 70-50=25x-21x\\ \\ \Rightarrow 4x=20\\ \\ \Rightarrow x = \frac{20}{4}=5$

Numbers are:
3x = 3×5 = 15
5x = 5×5 = 25
Numbers are 15 and 25.