Directions: Given below is a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements is sufficient to answer the question. You should use the given data and your knowledge of Mathematics to choose between the possible answer.
What is the time taken by Ram from point A to other point B?
I. If he walks 25% faster than his usual speed then he reaches 20 seconds earlier.
II. If he walks half of his usual speed, he takes 100 seconds more to reach the finishing point B.
III. If he walks one-fourth of his usual speed, he takes 300 seconds more to reach the finishing point B.
Solution
Correct Answer: Option D
Let speed = v, distance = x, time = t
Time(t) = Distance/ Speed = x/v
From statement I:
If he walks 25% faster than his usual speed then he reaches 20 seconds earlier.
Then speed = v + v × 25% = v + v/4 = 5v/4
Now according to the statement,
x/(5v/4) = t – 20
⇒ 4x/5v = t – 20
⇒ x/v = (5/4) × (t – 20)
⇒ t = (5/4) × (t – 20) [∵ x/v = t]
⇒ 4t = 5t – 100
⇒ t = 100 seconds
Statement I alone is sufficient to answer the question.
From statement II:
If he walks half of his usual speed, he takes 100 seconds more to reach the finishing point B.
⇒x/(v/2) = t + 100
⇒ 2x/v = t + 100
⇒ 2t = t + 100 [∵ x/v = t]
⇒ t = 100 seconds
Statement II alone is sufficient to answer the question.
From statement III:
If he walks one-fourth of his usual speed, he takes 300 seconds more to reach the finishing point B.
⇒ x/(v/4) = t + 300
⇒ 4x/v = t + 300
⇒ 4t = t + 300 [∵ x/v = t]
⇒ 3t = 300
⇒ t = 100 seconds
Statement III alone is sufficient to answer the question.
Hence, all statements I, II and III alone is sufficient to answer the question.
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