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Two numbers are in the ratio 2:3. If 4 be subtracted from each , they are in the ratio 3:5. The numbers are?
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Two numbers are in the ratio 2:3. If 4 be subtracted from each , they ...
Problem Statement:

Two numbers are in the ratio 2:3. If 4 be subtracted from each, they are in the ratio 3:5. The numbers are?


Solution:

Let the two numbers be 2x and 3x.

When 4 is subtracted from each number, the ratio becomes 3:5. This means:



  • The first number minus 4 is equal to 3k

  • The second number minus 4 is equal to 5k



So we can write:



  • 2x - 4 = 3k

  • 3x - 4 = 5k



We can solve for k by multiplying the first equation by 5 and the second equation by 3, and then equating the two:



  • 10x - 20 = 15k

  • 9x - 12 = 15k



Equating the two, we get:



  • 10x - 20 = 9x - 12

  • x = 8



So the two numbers are:



  • 2x = 16

  • 3x = 24



Therefore, the two numbers are 16 and 24.


Answer:

The two numbers are 16 and 24.
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Two numbers are in the ratio 2:3. If 4 be subtracted from each , they are in the ratio 3:5. The numbers are?
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