Question

two numbers are in the ratio 3:6. if each is increased by 5 the new ratio is 2:3

Answer 1

hey!!!

according to the question, two numbers are in ratio 3 : 5

let the two numbers be 3x and 5x.

if each number is increased by 5, then the new ratio will become 2 : 3

therefore 3x+5/5x+5 = 2/3
>> 3(3x+5) = 2(5x+5)
>> 9x + 15 = 10x + 10
>> 9x - 10x = 10 - 15
>> -x = -5
>> x = 5

hence, the two numbers are :-
3x = 3 × 5 = 15 and 5x = 5 × 5 = 25

cheers!!!

Answer 2

Should be 3:5
$let \: x \: and \: y \: be \: the \: two \: numbers \\ we \: have \\ \frac{x}{y} = \frac{3}{5} \\ = > x = \frac{3y}{5} \: \: - - - (1) \\ from \: question \\ \frac{x + 5}{y + 5} = \frac{2}{3} \\ = > 3x + 15 = 2y + 10 \\ = > 3( \frac{3y}{5} ) + 15 = 2y + 10 \\ = > \frac{9y}{5} + 15 = 2y + 10 \\ = > \frac{9y}{5} - 2y = 10 - 15 \\ = > \frac{9y - 10y}{5} = - 5 \\ = > \frac{ -y}{5} = - 5 \\ = > -y = - 25 \\ = > y = 25 \\ putting \: y = 25 \: in \: (1) \\ x = \frac{3 \times 25}{5} \\ = > x = 15 \\ hence \: the \: two \: numbers \: are \: 25 \: and \: 15$