Pls answer it experts

Question

Three numbers are in the ration 3:7:9. If 5 is subtracted from the second the resulting numbers are in AP. Find the original no .

Answer 1

Let the three numbers which are in the ratio 3:7:9 be 3x,7x and 9x.

Now, on subtracting 5 from the second number, we get the

Three numbers as 3x, 7x-5 and 9x

Since, these numbers are in AP, therefore, we have

2(7x-5) = 3x+9x

14x-10 = 12x

2x=10

x=5

Hence, the three original numbers are 3x =15, 7x=35 and 9x =45

2nd Method

Since, these numbers are in AP, therefore, the common differences between them will be same, we have

7x-5-3x = 9x-7x+5

4x-5 = 2x+5

2x = 10

x = 10/2 = 5

x=5

Hence, the three original numbers are 3x =15, 7x=35 and 9x =45

Comments

Why u multiplied 7x- 5 by 2

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because as three numbers are in AP, so the sum of 1st and last term will be the double of the middle term.

You may also follow the 2nd method I have mentioned as if three numbers are in AP then the common differences will be same