Question

Pls answer this question, It is from ratio and proportion

Answer 1

Answer:

We can actually solve this one using variables.

Let us take the two numbers as x and y.

Given x: y = 12 : 13

⇒ x/ y = 12/ 13 ( as ratio denotes division )

⇒ 13x= 12y

⇒ x= 12y/ 13 ------ (1)

Now each number is reduced by 20.

So we have x-20 and y-20.

Given, ratio = 2:3

So we have x-20/ y-20 = 2/3

Therefore, 3(x-20) = 2(y-20)

           ⇒   3x - 60 = 2y - 40

           ⇒   3x- 2y = 20

           ⇒   3 (12y/13) -2y = 20 -----[ from (1) ]

           ⇒  36y/13 -2y = 20

           ⇒  (36y- 26y)÷13 = 20

           ⇒ 10 y = 20× 13

           ⇒ y = 26

Therefore x= 12y/ 13 = (12 ×26)/13 = (12 ×2)= 24

Let's verify.

Given, x/ y= 12/ 13

So we have 24/26, which can be exactly simplified to 12/13.

Also x-20/ y-20= 2/3

So we have 4/6. That is also equal to 2/3.

Hence our answer is correct. The option is (c).