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

Answer:

48

Step-by-step explanation:

Given 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)

We have 3/2 : 8/3(convert mixed fraction)

We need to find x/y. So taking lcm of 2 and 3 we get 6

So 3/2 x 6 = 8/3 x 6 = 9:16

x/y = 9/16

16 x - 9 y = 0

Now when increased by 15 we get

x + 15 / y + 15 = 5/3 : 5/2 (convert mixed fraction)

Again 6 is lcm so we get 5/3 x 6 = 5/2 x 6 = 10 /15

So x + 15 / y + 15 = 10 / 15 = 2/3

So we get 3 x + 45 = 2 y + 30

3 x - 2 y = - 15

Solving two equations we get

3 x - 2 y = - 15  x 9

16 x - 9 y = 0    x 2

----------------------------

27 x - 18 y = - 135

32 x - 18 y = 0

----------------------------

- 5 x = - 135

x = 27

3 x - 2 y = - 15

3(27) - 2 y = - 15

81 - 2 y = - 15

 - 2 y = - 96

  y = 48

So the two numbers are 27 and 48.

Answer 2

Answer:

a & b = 27 & 48

Step-by-step explanation:

Let say two numbers are a & b

a/b  = (3/2)/(8/3)

=> a/b = 9/16

=> 16a = 9b  

=> 16a - 9b = 0   - eq 1

(a+15)/(b+15) = (5/3)/(5/2)

=> (a+15)/(b+15) =2/3

=> 3a + 45  = 2b + 30

=> 3a - 2b = - 15  - eq2

2*eq1 - 9 eq2

5a = 135

=> a = 27

16 * 27  - 9b = 0

=> b = 48

a & b = 27 & 48