Six cities of India – Jammu, Kolkata, Lucknow, Mumbai, Nagpur and Orcha are connected by one way and two way highways as indicated in the diagram given below. The arrow head indicates the direction in which the traffic is allowed to flow. No other route is available except those given in the diagram.
What is the least possible number of cities, a person has to pass through, while travelling from Mumbai city to Lucknow city?
Following are the possible ways from city Mumbai to city Lucknow.
I. Mumbai – Nagpur – Kolkata –Lucknow
II. Mumbai – Jammu – Orcha – Lucknow
III. Mumbai – Nagpur – Jammu – Orcha – Lucknow
The least possible number of cities is two.
<p>Following are the possible ways from city <em>Mumbai </em>to city <em>Lucknow</em>.</p><p><!- [if !supportLists]->I. <!- [endif]-><em>Mumbai – Nagpur – Kolkata –Lucknow</em></p><p><!- [if !supportLists]->II. <!- [endif]-><em>Mumbai – Jammu – Orcha – Lucknow</em></p><p><!- [if !supportLists]-><em>III. </em><!- [endif]-><em>Mumbai – Nagpur – Jammu – Orcha – Lucknow</em></p><p>The least possible number of cities is two.</p>
From the 1st statement: B2 is now as old as B3 was in the past. Hence B2 is younger to B3 or B2 < B3. Also sometime in the past B1 was twice as old as B4. So B1 is elder to B4 or B1 > B4. B3 will be as old as B5 in future, hence B3 < B5. The second statement suggests: B1 > B6. B1 was as old as B7 in the past. Hence B1 > B7. B4 will be as old as B6 in future. Hence B6 > B4. B6 will be as old as B7 now in future. Hence B7 > B6. B7 was as old as B2, when B1 was as old as B7. Hence B1 = B2. Combining both the results, we get: and B5 > B3 > B2 = B1 > B7 > B6 > B4 (Note by B1 = B2, it is meant that they are of similar age group, not necessarily the same).
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