The villages P, Q, R and S are situated, not necessarily in that order, on a long straight road. The distance from P to R is 75 km, the distance from Q to S is 45 km and the distance from Q to R is 20 km. Which of the following could not be the distance, in km, from P to S?
A 10 B 50 C 80 D 100 E 140
C
Since the distance from P to R is 75 km and the distance of Q from R is 20 km, there are two possible distances of Q from P, (75 + 20) km = 95 km and (75 − 20) km = 55 km. For each of the possible positions of Q, there are two possible positions of S, each 45 km from Q, as shown in the diagrams below.
Therefore the possible distances, in km, of S from P are 95 + 45 = 140, 95 − 45 = 50, 55 + 45 = 100 and 55−45 = 10. Therefore, of the options given, the one which is not a possible distance in km of S from P is 80.
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