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11 Jul 2026, 06:25
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We know that,
There are 2 activities: Swimming and Cardio machine workouts
Total members = 420
Let the memebrs be divided into 4 groups
Both, Cardio only, Swimming only and Neither
We are given that,
Members who met mark for both = 160
Members who met mark for cardio only = 80
Let members who met mark for swimming only = x
Members who met mark for neither = y which we need to find out
=> x + 80 + 160 + y = 420
=> x + y = 180
We are given that, for every member who met neither activity, 5 met swimming only
=> x = 5y
=> x + y = 180
=> 5y + y = 180
=> y = 30
A. 30
There are 2 activities: Swimming and Cardio machine workouts
Total members = 420
Let the memebrs be divided into 4 groups
Both, Cardio only, Swimming only and Neither
We are given that,
Members who met mark for both = 160
Members who met mark for cardio only = 80
Let members who met mark for swimming only = x
Members who met mark for neither = y which we need to find out
=> x + 80 + 160 + y = 420
=> x + y = 180
We are given that, for every member who met neither activity, 5 met swimming only
=> x = 5y
=> x + y = 180
=> 5y + y = 180
=> y = 30
A. 30
11 Jul 2026, 06:25
Kudos
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t = total
s = only swimming
c = only cardio
b = both
n = neither
t = 420
b = 160
c = 80
s = 5n
t = s + c + b + n
420 = 5n + 80 + 160 + n
6n = 180
n = 30
IMO A
s = only swimming
c = only cardio
b = both
n = neither
t = 420
b = 160
c = 80
s = 5n
t = s + c + b + n
420 = 5n + 80 + 160 + n
6n = 180
n = 30
IMO A
11 Jul 2026, 06:43
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| Swim 2 hour mark | Swim not met 2 hour | Total | |
| cardio met 2 hour | 160 | 80 | 240 |
| cardio not met 2 hour | 5X | ??? X | 180 |
| Total | 420 |
Given in green
So, 6X = 180
X = 30
Answer: A
11 Jul 2026, 06:44
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There are a total of 420 people surveyed for Swimming and Cardio-machine workouts.
People who do both- 160
People who do only cardio-machine workouts- 80
For every one person that does neither, 5 people do only swimming.
We need to find ppl who do neither of the two.
Let,
people who do neither = N
For every one person that does neither, 5 do swimming.
Therefore, people who do only swimming- 5N
Total participants = People who do both + People who do neither + People who do just swimming + People who do just cardio
420=160+N+5N+80
6N=180
N=30
Ans- (A)
People who do both- 160
People who do only cardio-machine workouts- 80
For every one person that does neither, 5 people do only swimming.
We need to find ppl who do neither of the two.
Let,
people who do neither = N
For every one person that does neither, 5 do swimming.
Therefore, people who do only swimming- 5N
Total participants = People who do both + People who do neither + People who do just swimming + People who do just cardio
420=160+N+5N+80
6N=180
N=30
Ans- (A)
