Question

6) The ratio between two numbers is 12:13. If
each number is reduced by 20, the ratio
becomes 2:3. Find the numbers.​

Answer 1

Answer:

24 and 26 are the numbers

Step-by-step explanation:

the ratio given is 12:13 which can also be written as 12x/13x

if we reduce them by 20 we get 12x-20/13x-20 = 2/3

if we cross multiply it we will get 3(12x-20)=2(13x-20)

=36x-60=26x-40

if we simplify we get 36x-26x=-40+60

=10x=20

=x=20/10

x=2  

therefore 12x=12*2=24 and 13x=13*2=26

hope it helps ☺

Answer 2

$\\ \\ \large\underline{ \underline{ \sf{ \red{given:} }}}$

• Ratio between two numbers is 12:13.

• When each number is reduced ny 20 , ratio becomes 2:3.

$\\ \\ \large\underline{ \underline{ \sf{ \red{to \: find:} }}}$

• The two numbers.

$\\ \\ \large\underline{ \underline{ \sf{ \red{solution:} }}}$

Let the two numbers be 12x and 13x as ratio is 12:13.

_______________

Now , each number is reduced by 20 , then ratio becomes 2:3.

→ Numbers are (12x-20) and (13x-20)

→ Ratio of these numbers is 2:3.

$\\ \\ \sf \: \frac{12x - 20}{13x - 20} = \frac{2}{3} \\ \\ \\ \sf \: 3(12x - 20) = 2(13x - 20) \\ \\ \\ \sf \: 36x - 60 = 26x - 40 \\ \\ \\ \sf \: 36x - 26x = - 40 + 60 \\ \\ \\ \sf \: 10x = 20 \\ \\ \\ \boxed{ \bf \: \green{x = 2 }}$

Numbers are :-

• 12x = 12(2) = 24

• 13x = 13(2) = 26

Hence , numbers are 24 and 26.