On a certain assembly line, rejection rate for Hyundai i - 10 production was 4…
2024
On a certain assembly line, rejection rate for Hyundai i - 10 production was 4 percent, for Hyundai i - 20 production 8 percent and for the 2 cars combined 7 percent. What was the ratio of Hyundai i - 10 and Hyundai i- 20 production?
- A.
3/1
- B.
2/1
- C.
1/1
- D.
1/3
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Correct answer: D
Answer: 1 : 3
Let the number of Hyundai i-10 cars be x and the number of Hyundai i-20 cars be y.
Rejected i-10 cars = 4x/100; rejected i-20 cars = 8y/100.
Combined rejection rate is 7%, so (4x/100 + 8y/100)/(x + y) = 7/100. Multiplying both sides by 100 gives 4x + 8y = 7(x + y).
Solve the equation: 4x + 8y = 7x + 7y → 8y - 7y = 7x - 4x → y = 3x.
Therefore the ratio of Hyundai i-10 to Hyundai i-20 production is x:y = 1:3.
Check: if x = 1 and y = 3, combined rejection = (4%*1 + 8%*3)/(1+3) = (0.04 + 0.24)/4 = 0.07 = 7%, which matches the given value.