Two positive integers that have a ratio of 3:5 are increased in

Question

Two positive integers that have a ratio of 3:5 are increased in a ratio of 1:1. Which of the following could be the resulting integers?

(A) 3 and 5
(B) 5 and 13
(C) 21 and 30
(D) 34 and 68
(E) 75 and 45

divyadna · Answer

We can try plugging in the answer options for solving this question.

Let's start with option C i e. 21 and 30 be the resultant integers.
21-x/30-x=3/5
105-5x=90-3x
2x=15
x=7.5
21-7.5= 13.5
30-7.5= 22.5
13.5/22.5= 135/225= 3/5
It's a match.
Answer is option C

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Noida · Answer

Bunuel  Request for a solution

Bunuel · Answer

When two  positive integers  are  increased  in a ratio of 1:1, it implies that the  same positive number  was added to both of them. Given that the previous ratio was 3:5, which is less than 1, adding the same number to both the numerator and the denominator will increase the value of the new ratio, bringing it closer to, but still less than 1. Only option C fits this criterion.

Hope it helps.

sayan640 · Answer

Option B is also less than 1 . Why not option B or option D ?  Bunuel   MartyMurray

Bunuel · Answer

Please read carefully.

sayan640 · Answer

In the case of B and D also , values are getting increased . Not sure what I am missing. 😪

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Bunuel · Answer

Current ratio = 3/5 > 1/2. (B) = (5/13 < 1/2) < 3/5. (D) = (34/68 = 1/2) < 3/5 (C) = (21/30 = 7/10) > (3/5 = 6/10)

sayan640 · Answer

Thank you  Bunuel  ..Understood now..It was easy actually.

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hr1212 · Answer

Hi  Bunuel ,

By similar logic I was also able to drill it down to C that the ratio should increase but somehow algebra isn't holding true for this option. Can you please explain what am I missing here?

Let original numbers be 3x and 5x and let y be the number added.

Then resulting numbers are 3x + y and 5x + y

If we subtract these 2 numbers, we should get 2x and hence the values of initial numbers.

So for C, it would be 2x = 30 - 21 = 9 => x = 4.5

This results into initial numbers being (3*4.5 , 5*4.5) = (13.5, 22.5). These numbers are definitely not integers as mentioned in the question in which case this answer choice would also be invalid.

Regor60 · Answer

30 and 21 aren't necessarily the numbers but could be a partially reduced fraction of the original numbers, for example, 300 and 210

ManifestDreamMBA · Answer

I also did the same thing and eliminated C but figured none of the answer choices worked. So, pivoted to the fraction approach but lost a lot of time. It would be good to know why this method failed.

hr1212 · Answer

In which case question should have asked for the ratio of the resulting integers and not the exact integers. Because if we solve for the exact integers, then I don't think any of these answer choices are correct.

ManifestDreamMBA · Answer

After some afterthought, I believe that the numbers in option should have been 21 and 31. Reasons below:
1. The addition is for the positive integers and the rule where the ratio moves closer to 1 works when a positive integer is added to both numerator and denominator
2. Since 21 and 31 are the actual integers, not reduced forms. Trying when will this be 3:5 after removing a positive integer from both. 21-6 = 15 and 31-6 = 25, which makes the ratio 3:5

Two positive integers that have a ratio of 3:5 are increased in

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Two positive integers that have a ratio of 3:5 are increased in

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