Question

two numbers are in the ratio 4:5 . If 7 is subtracted from each other of them, then the ratio becomes 3:4. find the numbers​

Answer 1

Answer:

28 and 35

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Step-by-step explanation:

Let the numbers be a and b.

We are given

a / b = 4 / 5

and

( a - 7 ) / ( b - 7 ) = 3 / 4.

Multiplying these out, these can be rewritten as

5a - 4b = 0            (1)

and

4a - 28 = 3b - 21  <=>  4a - 3b = 7          (2)

There are many techniques for solving simultaneous equations like this.  Use your favourite.  One way is like this:

Multiply the equation (1) by 3 and equation (2) by 4 so the b's have the same coefficient:

15a - 12b = 0

16a - 12b = 28

Now subtract the first of these from the second:

a = 28

Using (1), we get

b = 5 × a / 4 = 5 × 28 / 4 = 5× 7 = 35.