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26 Dec 2025, 06:14
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We are given that,
Total people = 250
Let,
Total number of smokers = x
Total number of drinkers = y
30% both smokers and drinkers = 0.3 * 250 = 75
40% of the smokers do not drink
=> Number of smokers who drink => 0.6*x = 75
=> x = 125
=> Number of smokers that dont drink = 0.4*x = 0.4 * 125 = 50
25% of the drinkers do not smoke
=> 75% of drinkers smoke
=> 0.75* y = 75
=> y = 100
=> Number of drinkers who dont smoke = 0.25 * 100 = 25
We need to find percentage of non smokers that dont drink
=> Total number of people = Smoker/Drinkers + OnlySmokers + OnlyDrinkers + Non Smoker/Drinkers
=> 250 = 75 + 50 + 25 + Non S/D
=> Non S/D = 100
We also know that, total number of nonsmokers = 250 - x = 250-125 = 125
=> Percentage of nonsmokers who dont drink = 100/125 = 0.8 => 80%
E. 80%
Total people = 250
Let,
Total number of smokers = x
Total number of drinkers = y
30% both smokers and drinkers = 0.3 * 250 = 75
40% of the smokers do not drink
=> Number of smokers who drink => 0.6*x = 75
=> x = 125
=> Number of smokers that dont drink = 0.4*x = 0.4 * 125 = 50
25% of the drinkers do not smoke
=> 75% of drinkers smoke
=> 0.75* y = 75
=> y = 100
=> Number of drinkers who dont smoke = 0.25 * 100 = 25
We need to find percentage of non smokers that dont drink
=> Total number of people = Smoker/Drinkers + OnlySmokers + OnlyDrinkers + Non Smoker/Drinkers
=> 250 = 75 + 50 + 25 + Non S/D
=> Non S/D = 100
We also know that, total number of nonsmokers = 250 - x = 250-125 = 125
=> Percentage of nonsmokers who dont drink = 100/125 = 0.8 => 80%
E. 80%
26 Dec 2025, 06:37
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| Smokers | Non-Smokers | Total | |
| Drinkers | 30x | 0.25b | b |
| Non-Drinkers | 0.4a | y | |
| Total | a | z | 100x |
The above table is based on the data provided in the stem. I don't need the total number of people because I believe that this can be solved using percentags alone. Additional constants have been included.
Based on the info, Smokers who also drink i.e. 30x should be equal to 0.6a
Solving, we get a = 50x
That means z = 100x-50x = 50x
Next, Drinkers who smoke i.e. 30x = 0.75b
Solving, we get b = 40x
That would mean 0.25b = 10x
Since we need y, using the calculated info, y = z - 0.25b = 50x - 10x = 40x
Percentage of non-smokers who do not drink = y/z = 40x/50x = 0.8 or 80%
msignatius
26 Dec 2025, 06:38
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For this, I'd insist you draw a table, as I did when I solved this, but there's some basic one-or-two-line algebra that'll help directly solve this as well. Just in keep in mind what the question needs -solved.
Out of 250, 30% are both smokers and drinkers. That's 75 people accounted for, great. The rest will be split among just-drinkers, just-smokers, and teetotallers (those who abstain from both).
Now, we can bring in a couple of variables - x for the total number of smokers and y for the total number of drinkers. If 40% of the x's don't drink, that means 60% of the x-es drink, which is just your 75 we found above. With this we can back solve: 0.6x = 75; or x = 125 (total number of smokers).
Exactly the same can be done for the drinkers - if 25% of the ys don't smoke, that means 75% of them do, and 0.75y = 75, and y is simply 100 (total numbers of drinkers).
Clearly, 225 out of the 250 people indulge, and the very few - 25 don't.
But what is the question asking us to find?
"What percentage of non-smokers don't drink"
Clearly, we know that x, or number of smokers = 125, so 250 - 125 = 125 are the number of non-smokers.
Out of these non-smokers - 125 - we know that 25% of y (or just 25) are drinkers, so we minus that as well to get the true count of non-smokers who don't drink = 125 - 25 = 100.
Clearly, 100 (non-smokers who don't drink) are 80% of 125 (total non-smokers).
That's your answer - E.
Out of 250, 30% are both smokers and drinkers. That's 75 people accounted for, great. The rest will be split among just-drinkers, just-smokers, and teetotallers (those who abstain from both).
Now, we can bring in a couple of variables - x for the total number of smokers and y for the total number of drinkers. If 40% of the x's don't drink, that means 60% of the x-es drink, which is just your 75 we found above. With this we can back solve: 0.6x = 75; or x = 125 (total number of smokers).
Exactly the same can be done for the drinkers - if 25% of the ys don't smoke, that means 75% of them do, and 0.75y = 75, and y is simply 100 (total numbers of drinkers).
Clearly, 225 out of the 250 people indulge, and the very few - 25 don't.
But what is the question asking us to find?
"What percentage of non-smokers don't drink"
Clearly, we know that x, or number of smokers = 125, so 250 - 125 = 125 are the number of non-smokers.
Out of these non-smokers - 125 - we know that 25% of y (or just 25) are drinkers, so we minus that as well to get the true count of non-smokers who don't drink = 125 - 25 = 100.
Clearly, 100 (non-smokers who don't drink) are 80% of 125 (total non-smokers).
That's your answer - E.
Bunuel
26 Dec 2025, 06:44
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Assume ven diagram of Smoker and drinkers
a is only smoker
c as both smoker plus drinker
b only drinker
d neither of both
we got 40% of 250 i.e. 75 as both
so C = 75
now 40%(a+c) = a
so 2c = 3a
a = 50
now given (b+c) 0.25 = b
c = 3b
b = 25
and
a+b+c+d = 250
therefore d = 100
We need
d/(b+d) * 100
that is 80%
Hence E answer
a is only smoker
c as both smoker plus drinker
b only drinker
d neither of both
we got 40% of 250 i.e. 75 as both
so C = 75
now 40%(a+c) = a
so 2c = 3a
a = 50
now given (b+c) 0.25 = b
c = 3b
b = 25
and
a+b+c+d = 250
therefore d = 100
We need
d/(b+d) * 100
that is 80%
Hence E answer
