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Question

Directions:- Study the following information carefully to answer the question given below.

A, B, C, D and E are the five towns out of which two are hill stations and the rest are in plains. Two towns which are in plains have harbours. Four towns out of five are capitals and two are industrial towns. The population of town is less than 5 lakh. It is 20 lakh of one town and more than 50 lakh of two towns. Two towns are on the same latitudes and the other two are on the same longitudes. Latitudes and longitudes of both the harbours are different and out of these, one is an industrial town. The population of both the industrial towns is more than 50 lakh. The longitudes of one hill station and one of the industrial towns are same. The latitudes and longitudes of the other hill station and the other harbour are different. One industrial town is neither a hill station nor a harbour. None of the hill stations is an industrial town. The hill station of which longitude is the same as that of a harbour, is a capital. B is a hill station while the longitudes of A and E are same. E is a harbour. The latitude of D and C are same and the population of D is 20 lakhs. Both the harbours are capitals one of them is an industrial town.

Which of the following two towns have a population less than 5 lakhs?

A
D and A
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B
B and C
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C
A and B
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D
A and C
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E
None of these
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Solution

The correct option is C A and B
The given information is:-
(i) 2 hill stations, 2 harbours in plain, 3 in plains.
(ii) 4 capitals
(iii) 2 industrial towns.
(iv) One harbour is an industrial town.
(v) One industrial town is neither a hill station nor a harbour.
(vi) No hill station is an industrial area.
(vii) The hill station, of which longitude is the same as that of the harbour, is a capital.
(viii) The population of both the industrial town is more than 50 lakhs.
(ix) One harbour is an industrial area.
(x) The longitude of one hill station and one of the industrial towns are the same.
(xi) The latitudes and longitudes of the other hill stations and the other harbour are different.
(xii) Longitudes of A and E are same.
(xiii) E is a harbour.
(xiv) Latitudes of D and E are the same.
(xv) Population of D is 20 lakh.
(xvi) Both the harbour are capitals and one of them is an industrial town..

Now from (x), (xii) and (xiii), A must be a hill station and from (vii), A must also be a capital. We know that A and B are hill stations while E is a harbour (from xiii). From (xv) and (viii), D cannot be an industrial area. D cannot be a hill station too because only two hill stations A and B are already there. So, D must be a harbour. Hence, C, the only town remaining, must be an industrial town. So, we have now the following conclusions:-
(i) A and B are hill station and their population is less than 5 lakhs.
(ii) C is an industrial town but not a harbour and its population is more than 50 lakhs.
(iii) D is a harbour but not an industrial town and its population is 20 lakhs.
(iv) E is a harbour and industrial town and its population is more than 50 lakhs.
(v) Capital towns are - A, C, D and E.

A and B towns have a population less than 5 lakh.
Hence, required answer is (C)

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