Mr. Ambrose and Mr. Bruford, two senior executives of a London based multinational organisation, embarked on a business tour during the course of the year 2003 A.D. to two of the branches of the organisation located in the capital cities of two different countries. The flag of the country visited by Mr.Ambrose included a blue trapezoid and a green trapezoid as two of its features while the flag of the country corresponding to the city visited by Mr. Bruford contained a purely red circle.
Immediately upon reaching the capital city of the host country, Mr. Ambrose reset his 24 hour wristwatch in accordance with the local time and observed that the date according to his watch was Pth day of the Qth month of 2003, where 2003 when divided separately by P and Q yielded a remainder of 3 in both the cases; both P and Q were greater than 3, and (P+Q) was divisible by 5. Furthermore, it was a FRIDAY according to his watch.
After reaching his hotel room, when it was precisely (x^2) Hours according to his watch, Mr. Ambrose contacted Mr. Bruford for an urgent matter whereby he learnt that the time according to Mr. Bruford's 24 Hour electronic wristwatch (which was also reset in accordance with the local time) at the same instant was exactly ((5/4)*x² +2) hours.
Later during the same day, after returning from an important business meeting to his hotel room, Mr.Ambrose's watch displayed exactly ((5/4)*x²+2) Hours when Mr. Ambrose contacted Mr.Bruford for the second time to discuss the outcome of their respective business meetings; Mr. Bruford's response included the fact that the time by his watch was exactly x Hours.
What cities were visited by Mr. Ambrose and Mr.Bruford? What was the date and time according to their respective wristwatches when Mr. Ambrose contacted Mr. Bruford for the second time?
Note: This problem is based on the global political scenario prevailing in 2003 A.D.
Submitted by K Sengupta
Rating: 1.5000 (2 votes)
# Mr. Ambrose was visiting DJIBOUTI while Mr. Bruford was visiting TOKYO.
# The respective time and date according to Mr. Ambrose's watch and Mr. Bruford's watch, the second time Mr. Ambrose contacted Mr. Bruford, were 22:00 Hours on 10 OCTOBER, 2003 and 04:00 Hours on 11 OCTOBER, 2003.
Since, we know that the Capital City of Japan is TOKYO, it follows that:
A year contains 12 months and any given month can contain at most 31 days, implying that P < = 31 and Q < = 12. Since 2003 when divided separately by P and Q leaves a remainder of 3, it follows that P and Q are factors of 2000 and P,Q > =4 (given).
Accordingly, the valid values of P and Q satisfying 4 < = P < = 31 and 4 <= Q < = 12 are given by:
P = 4,5,8,10,16,20,25
Q = 4,5,8,10
We recall that the day of the week according to Mr. Ambrose's wristwatch was FRIDAY ( in 2003 A.D.).
Accordingly, analysing the situation in light of the valid values of P and Q, we observe that the following constitute the probable dates in accordance with Mr. Ambrose's wristwatch:
4 APRIL( P=4,Q=4); 25 APRIL (P=25, Q=4); 16 MAY ( P=16,Q=5); 8 AUGUST ( P=Q=8) and 10 OCTOBER ( P=Q=10).
From the above, we observe that (P+Q) is divisible by 5 corresponding to 10 OCTOBER where P+Q =20 and none of the other dates satisfy conditions of the problem. Consequently, the date by Mr. Bruford's watch when he reached the Capital City of the host country was 10 OCTOBER.
Now, the second time Mr. Ambrose contacted Mr. Bruford. the respective times by Mr. Ambrose's watch and Mr. Bruford's watch were ((5/4) *(x^2) + 2 ) Hours and x Hours.
This is possible only if the date by Mr. Bruford's watch was precisely a day ahead of the corresponding date by
Mr. Ambrose's watch.
Accordingly, we have:
( (5/4) *(x^2) + 2 ) - (x^2) = (x+24) - ( (5/4) *(x^2) + 2 )
Or, 3*(x^2) - 2x - 40 = 0
Or, (x-4)(3*x + 10 ) = 0
Or, x = 4 ( ignoring the negative value of x which is inadmissible).
so that, (5/4) *(x^2) + 2 = 22 and x^2 = 16.
Hence, the time in the country visited by Mr. Bruford is 22-16 = 6 Hours faster on the time in the country visited by Mr. Ambrose.
Accordingly, the respective time and date according to Mr. Ambrose's watch and Mr. Bruford's watch, the second time Mr. Ambrose contacted Mr. Bruford, were 22:00 Hours on 10 OCTOBER, 2003 and 04:00 Hours on 11 OCTOBER, 2003.
We know that DJIBOUTI is the only country whose flag's features inter-alia comprise a blue trapezoid and a green trapezoid and consequently, the country visited by Mr. Ambrose was DJIBOUTI whose Capital City is also called DJIBOUTI.
Mr. Bruford's destination country is 6 Hours ahead of DJIBOUTI, and accordingly, the said country could be South Korea, North Korea or Japan each of whose flag's features include a circle.
Among these, a circle which is purely Red in colour is only observed in Japan's Flag while the circle appearing in South Korea's flag is coloured Red and Violet and the circle in North Korea's Flag is coloured white with a Red Star inscribed within.
Mr. Ambrose was visiting DJIBOUTI while Mr. Bruford was visiting TOKYO.
The respective time and date according to Mr. Ambrose's watch and Mr. Bruford's watch, the second time Mr. Ambrose contacted Mr. Bruford, were 22:00 Hours on 10 OCTOBER, 2003 and 04:00 Hours on 11 OCTOBER, 2003.