Question

becomes 7: 15?
12. Two numbers are in the ratio 7:11. If 7 is added to each of the numbers, the ratio becomes
2:3. Find the numbers.
13. Two numbers are in the ratio 5:9. On subtracting 3 from each, the ratio becomes 1:2. Find​

Answer 1

Answer:

12]. The numbers are 49 and 77

13]. The numbers are 15 and 27

Step-by-step explanation:

12]

As the numbers are in the ratio 7:11, we can assign them as 7x and 11x.

ATQ,

7x + 7 : 11x + 7 = 2:3

∴ (7x + 7)/(11x + 7) = 2/3

∴ 3(7x + 7) = 2(11x + 7)

∴ 21x + 21 = 22x + 14

∴ 22x - 21x = 21 - 14

∴ x = 7

Thus, the numbers are 7*7 and 11*7, or 49 and 77

The required numbers are 49 and 77

13]

As the numbers are in the ratio 5:9, we can assign them as 5x and 9x.

ATQ,

5x -3 : 9x - 3 = 1:2

∴ 2(5x - 3) = 1(9x - 3)

∴ 10x - 6 = 9x - 3

∴ 10x - 9x = -3 + 6

∴ x = 3

Thus, the numbers are 5*3 and 9*3, or 15 and 27

The required numbers are 15 and 27.