Question

two numbers are in the ratio 1(1/2) :2(2/3) when each of these increased by 15,they become in the ratio 1(2/3):2(1/2)

Answer 1

two numbers are in the ratio 1(1/2) :2(2/3) when each of these increased by 15,they become in the ratio 1(2/3):2(1/2)

ratio given

3/2 : 8/3

multiplying by 6 both sides

9 : 16

let say first number 9k

then second number 16k

new ratio

(9k +15) : (16k + 15) :: 5/3 : 5/2

(9k +15) : (16k + 15) :: 2 : 3

(9k +15) / (16k + 15) = 2 / 3

27k + 45 = 32k + 30

5k = 15

k = 3

numbers 27 & 48

verification

dividing by 18

3/2 : 8/3

adding 15

42 & 63

dividing by 21/5

5/2 : 5/3

Answer 2

Answer:

27/48 = 9/16

Step-by-step explanation:

Let us convert the given mixed fraction into simplest fraction.

1(1/2) = 3/2

2(2/3) = 8/3

In order to solve the given question, let us assume that the required numbers are  x and y. Then, according to question:

x/y = (3/2)/(8/3)

x/y = 9/16    ------------------------------------------------- equation  (1)

According to the question, 15 is added to each number. Hence the values of new numbers become

(x + 15) and (y + 15)

Also it is given that their new ratio become (5/3)/(5/2)

Hence, in mathematical terms

(x + 15 )/ (y+15) = (5/3)/(5/2)

(x + 15 )/ (y+15) = 2/3   ----------------------------------------------- equation (2)

Now we need to solve these simultaneous equations in x and y to get the required numbers. In order to solve for x and y, let us put the value of x from equation (1) into equation (2)

From equation (1), x = 9/16 y; putting this value in equation 2

{(9/16)y + 15} / (y + 15) = 2/3

Please find the detailed solution in the attachment.

CHECK:-

We have got our answer as 27/48 which in simplest ratio is 9/16 which satisfies the condition given in the question.

on adding 15 to each number

27 + 15 = 42

and 48 + 15 = 63

Taking ratio: 42/63 = 2/3 which also satisfies the question. Hence we can be sure that the answer is correct.