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In a province, there are three types of cities: A, B and C. The number of cities A is 30% more than that of cities B and C together. Number of cities B is 20% of total cities. If the total number of cities is 10000, then how many type C cities are there?

In a province, there are three types of cities: A, B and C. The number of cities A is 30% more than that of cities B and C together. Number of cities B is 20% of total cities. If the total number of cities is 10000, then how many type C cities are there? Correct Answer Given condition is not possible

Let number of cities C be T.

Number of cities B is 20% of total cities. Total number of cities is 10000.

⇒ Number of cities B = 10000 × (20/100) = 2000

⇒ Number of cities A and C = 10000 – 2000 = 8000

⇒ Number of cities A = 8000 – T

The number of cities A is 30% more than that of cities B and C together.

⇒ 8000 – T = (T + 2000) × (1 + 30/100)

⇒ 8000 – T = 1.3T + 2600

⇒ T = 5400/2.3

We see that T is not a natural number, and hence cannot be the number of cities C.

∴ Given condition is not possible.

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