What is the correct approach??

Forget this question. It is badly formulated.

First of all the OA is not 14 but 13/15. it is impossible to get a whole number from the statement above.

1/5 of the entire lot is red so 20 cars. Of this 2/3 ar convertible, which means that 13.3 cars are of this type. Which is impossible: you must have a whole number of cars.

Anyway, if we wanna solve we do have 13 cars not covertible over 15. The answer is 13/15.

Hope this helps.

PS: this is an easy question NOT hard.

Let's say we have 300 cars.

1/5 of them are red: 300*1/5 = 60
2/3 of the red cars are convertibles: 2/3*60 = 40
Meaning, 40 out of 300 cars ARE red convertibles. The fraction is 2/15
Question: What fraction of all the cars are NOT red convertibles?
15/15 - 2/15 = 13/15

We are not told that there are only 100 cars

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Let total car =a

Red= a/5
Red-Convertivle= a/5*2/3= 2a/15

therefore all the car those are not Red-Convertible= a- 2a/15= 13a/15

the ratio = 13/15 (answer)

i keep getting confused. Why can you not plug in 15 or 30 for amount of cars? I plug in 15 or 30 since it is divisible by 5 and 3. If i plug in these numbers i do not get the correct answer

Let's say we take 30 cars in total.

1/5 of all the cars on a certain auto lot are red. So total red cars will be \(\frac{30}{5}\) = \(6\)

\(\frac{2}{3}\) of all the red cars are convertibles. So red convertible = \(4\)

What we are asked is the ratio of the cars that are not red convertble.
So no of cars not red convertible = total cars - red convertibles \(= 30 - 4 = 26\)

Ratio = \(\frac{26}{30}\) = \(\frac{13}{15}\)

Please ask if the doubt remains.

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