The question below is followed by three statements I, II, and III. You have to determine whether the data given is sufficient for answering the question. You should use the data and your knowledge of mathematics to choose the best possible answer. A car travels from city P to city Q in T hours with a speed of v km per hour. Distance between cities P and Q is D kilometers. If it increases its speed by 5 kmph it saves some time. Find the actual speed of the car. Statement I: If the car travels from P to Q with its actual speed of v kmph and come back with the speed of v + 5 kmph in 2T – 0.6 hrs Statement II: A bus start form Q at the same time when the car starts from P and the speed of the bus is 50% more than the speed of the car and the bus meets car after covering 60% of the distance Statement III: Distance between PQ is given by D2 – 25D + 200 = 0  ?

Option 2 : Statement I and III are sufficient to answer the question.

Let after increasing speed by 5 kmph the car saves t time.

From question,

D/v = T   ----(i)

And D/(v + 5) = T – t   ----(ii)

Statement 1:

D/v + D/(v + 5) = 2T – 0.6

From (i) and (ii),

T + T – t = 2T – 0.6

⇒ t = 0.6 hours

Also D/v + D/(v + 5) = 2D/v – 0.6   ----(iii)

Statement 2:

0.4D/v = 0.6D/1.5v

⇒ 0.4 = 0.4

Statement 3:

D2 – 25D + 200 = 0

From here we will get the value D

After putting the value of D in equation (iii) we will get the value of v.

∴ The right answer will be option 2.