In a certain math class, one-tenth of the students cheated on a test

This question is slightly tricky if one reads it at one go. Conversion from words to maths is key to this question.
The question asks for the ratio of students cheated to a total no of students. Say, total= 100 students.
As per the question, one-tenth of the students cheated on a test and were caught. So 1/10th of total = 10 students.
Now comes the tricky part. The question states that 1/5th of the students who cheated (not the students) didn't get caught. Let S be students who cheated. So 1/5th of S didn't get caught that means 4/5th got caught. We already have 10 students who cheated and got caught.
4/5th of S=10. S=50/4. [S cannot be a fraction, but 100 was an arbitrary number, so ignore whatever value S has here].
Finally, Students cheated to total students = S/100 = (50/4)/100 = 1/8.
Hence, C is the correct answer.

Let the total number of students = 100
As per the below table structure,


10 + X/5 = X
--> 10 = 4X/5
--> X = 10*5/4 = 25/2

Number of students cheated = 25/2
--> Fraction of class cheated = 25/2/100 = 1/8

IMO Option C

let total students = 100
who cheated and got caught= 1/10 * 100 = 10
1/5th of students who cheated did not get caught so 4/5 of students cheated and got caught ; i.e 4x/5 =10 ; x= 50/4 students got caught
fraction ; 50/4* 1/100 = 1/8
IMO C

Let number of students = s
Let number of cheaters = c

Given: No. of cheaters who got caught = \(\frac{s}{10}\)
And, No. of cheaters who did not get caught = \(\frac{c}{5}\)

Therefore,
\(\frac{s}{10} + \frac{c}{5} = c,\)
\(\frac{s}{10} = \frac{4c}{5},\)
\(\frac{c}{s} = \frac{5}{40} = \frac{1}{8} \)

Hope this helps.

let the total number students = 40

lets number of students who cheated = x

1/10*40 = cheated+caught= 4 students

4/5(x)= 4

therefore total number of students who cheated= 5

ratio= 5/40= 1/8

option C is the correct option!
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lets say total no of students is 100
total nos of studetns who cheated is x
cheated and caught=1/10=10
cheated and not caught=x/5

therefore, 10+x/5=x, solving for x=12.5=1/8.Ans C

1/5th of cheated did not get caught = 4/5th of cheated got caught.

4/5th of cheated = 1/10th of Total

Cheated = 1/8th of Total

Answer (C)
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Let C = # of students who cheated

Let N = # of students who did not cheat

C + N = 100 students


C is further broken down into: (Cheated + Caught) and (Cheated + NOT Caught)


"1/10 of the students cheated AND were Caught"

thus: (Cheated + Caught) = (1/10) * 100 = 10

"1/5 of the students who cheated did NOT get caught"

C = # of students who cheated ------> thus: (1/5)C = (Cheated + NOT Caught)



adding the 2 groups together to make up all the people who cheated = C

10 + (1/5)C = C

10 = (4/5)C

C = 25/2


What fraction of the total students Cheated?

or

what is: C / T = ?


(25/2) / 100 = 25 / 200 = 1/8


answer C: 1/8

Let's assume there are 100x students.
Now, 10x cheated and were caught.
Now 10x = \(\frac{4}{5}*cheated\).
so cheated = 12.5x
and the proportion of cheated in class = \(\frac{12.5x}{100x}\) = \(\frac{1}{8}\)

2 x 2 grid method would be best for this problem.
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Always read word problems slowly

Assume 100 students
one tenth cheated and caught 10 no
one fifth of those cheated did not get caught so 4/5 th get caught
so four fifth caught equals to 10 no
so all of those cheated equals to 12.5 no ( fraction is ok as i have assumed 100 )

percentage of cheated = 12.5/100 =1/8

Since the fractions have 10&5 as denominators let's assume with the LCM 10as the number of total students. Then 1/10=1 is the number who cheated and got caught.
Let's assume C as the number of cheaters. Since 1/5 were not caught 4/5of C were caught and we know from the earlier step that this is 1
So 4/5(C)=1or C=5/4
So 5/4 out of total 10 students, cheated.
5/(4*10)=5/40=1/8
Hence C

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A better trick is to assume the number of people that did not get caught
Assume 1/5 that did not get caught as 2.
People who cheated and got caught=4*2=8
People who cheated and got caught were 1/10 of the students so Total students=10*8=80
Total no. of students who had cheated=10/80=1/8 (D)

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