A recent survey for Delhi showed that 44% of the families own only one car per…
2020
A recent survey for Delhi showed that 44% of the families own only one car per family, 25% of the remaining families own two cars per family and the rest of the population own three or more cars per family. Then, what is the percentage of families with three or more cars?
Answer: B. 42% — Concept: When a whole is split into successive categories where a later percentage is stated as a share of the remainder (not of the original total), first…
- A.
58%
- B.
42%
- C.
43%
- D.
31%
Attempted by 7 students.
Show answer & explanation
Correct answer: B
Concept: When a whole is split into successive categories where a later percentage is stated as a share of the remainder (not of the original total), first find the remainder after removing the earlier category, then apply the next percentage to that remainder — never to the original 100%. Whatever is left after all stated shares are removed is described as ‘the rest’.
Application:
Let the total number of surveyed families be 100%.
Families owning exactly one car = 44% of the total, so the remaining families = 100% − 44% = 56% of the total.
Families owning exactly two cars = 25% of this remaining 56%, i.e. (25/100) × 56% = 14% of the total.
Families owning three or more cars = remaining families − two-car families = 56% − 14% = 42% of the total.
Cross-check: 44% (one car) + 14% (two cars) + 42% (three or more) = 100%, so the three shares correctly account for the entire surveyed population.
Result: 42% of the families own three or more cars.
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