Question
A cyclist travels from town P to town Q at 12 km/h and
returns from Q to P by the same route at a speed which is 25% higher. Due to the increase in speed on the return journey, he takes 1 hour less for the entire trip than he would have taken if he had travelled at 12 km/h both ways. What is the distance between P and Q?Solution
ATQ, Let distance = d km. Time if speed is 12 km/h both ways = 2d/12 = d/6 hours. Actual speeds: P→Q: 12 km/h ⇒ time = d/12 Q→P: 25% more ⇒ 12 × 1.25 = 15 km/h ⇒ time = d/15 Actual total time = d/12 + d/15 = (5d + 4d)/60 = 9d/60 = 3d/20 Given: 3d/20 = d/6 − 1 Multiply by 60: 9d = 10d − 60 ⇒ d = 60 km.
Statement: T < U; W ≤ V = U; I > V; X ≥ U
Conclusion:
I. I > X
II. X ≥ I
Statement: F < G < H ≥ J; F ≥ K > L
Conclusion:
I. H > L
II. H = L
Statements:
C > D ≥ E ≤ F; Y ≥ Z ≥ A = C
Conclusion:
I. Y > F
II. F ≥ Y
Statements: L ≤ M = N ≤ O = Q; Z ≥ T > P = Q; L > R = S < V
Conclusions:
I. Z ≥ N
II. V > P
III. R < T
Statements: R = S ≥ T, U < Q < W = T, U = Z > V
Conclusions:
I. R > U
II. S ≥ Z
III. V < T
Statement: A > B = E < F > H; I ≤ D < C; H > G > C
Conclusions:
I. F > I
II. I < G
III. B < G
Statements: S < T < U ≤ W; C > U < V < W ≤ X
Conclusion:
I. S < V
II. T < X
Statements:S > T,T ≥ U,U < V
Conclusions: I. T > V II. S > U
Statements: N = Q < X ≤ L, L > T = G ≥ E
Conclusions:
I. L ≥ Q
II. G > X
III. L > N
In each of the questions below are given some statements followed by two conclusions. You have to take the given statements to be true even if they see...
