Question

Direction: Each of the questions below consists of a question and three statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and give answer:On a recent journey Aman drove from City A to city B to city C. His average speed for the whole journey was 60 km/hr. Find the average speed on his journey from city B to city C.Statement I:  Average speed during the journey from city A to city B is 48 km/hr Statement II: Total time taken for the entire journey is 3 hours Statement III: Ratio of distance travelled while going from A to B and B to C is 2 : 3

• (A) Either statement III alone or statements I and II together are sufficient.
• (B) Only statement III is sufficient.
• (C) Statement I and Statement II together are sufficient.
• (D) Statement I and Statement II together are sufficient.

Answer 1

The Correct Option is D

Explanation:
Given, on a recent journey Aman drove from City A to city B to city C. His average over the whole journey was $60km/hr$.From statement I, average speed during journey from city $A$ to city $B$ is $48km/hr$.From statement II, total journey time is 3 hoursFrom statement III, ratio of distance travelled while going from $A$ to $B$ and $B$ to $C$ is $2:3$.Thus, statement I and II and III or I and III are not sufficient to answer the question.From statement III,Let the distances to be covered be $2x$ and $3x$ respectively.Total distance covered $=2x+3x=5x$Average speed $=\frac{\text{ total distance }}{\text{ total time }}$$\Rightarrow \frac{5x}{3}=60$$\Rightarrow x=36km$Now, distance travelled from city $A$ to city $B=2x=72km$Let the time of this journey be ' $t$ '$\frac{72}{t}=48$$\Rightarrow t=1.5$ hoursThus, time taken for journey from city $B$ to city $C=3-1.5=1.5$ hoursDistance travelled in this journey $=3x=108km$Average speed on the journey from city $B$ to city $C$ $=\frac{108}{1.5}=72km/hr$Thus, statement I, II and III are together sufficientHence, the correct option is (D).