Question

Each question below is followed by two statements I and II. You have to determine whether the data given in the statements are sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answer.

What is the difference between the time taken by Kantesh and Sudesh to complete the journey?

I. Sudesh and Kantesh travelled through a boat and distance covered by them is equal, where the speed of stream is 5 km/hr, The ratio of downstream speed and upstream speed of Sudesh is 4 ∶ 3.

II. Kantesh's boat is 20% slower than Sudesh's boat. The midpoint between their location and destination is 66 km. Both travelled back to their original location to complete the journey.

1. If the data in statement I alone is sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
2. If the data in statement II alone is sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
3. If the data either in statement I alone or in statement II alone is sufficient to answer the question.
4. If the data even in both the statements I and II together are not sufficient to answer the question.
5. If the data in both statements I and II together are needed to answer the question.

Answer 1

Correct Answer - Option 5 : If the data in both statements I and II together are needed to answer the question.

Using statement I

Speed of stream = 5 km/hr

The ratio of downstream speed and upstream speed of Sudesh is 4 ∶ 3

⇒ (B + S)/(B – S) = 4/3

B → Speed of boat

S → Speed of stream

∴ (B + 5)/(B – 5) = 4/3

⇒ 3B + 15 = 4B – 20

⇒ B = 35 km/hr

∴ Speed of Sudesh = 35 km/hr

Statement I alone is not sufficient to answer the question

 

Using statement II

Kantesh's boat is 20% slower than Sudesh's boat

⇒ Let the speed of Sudesh be x km/hr

Then, speed of Kantesh = (80/100) × x = 4x/5

The midpoint between their location and destination is 66 km

Total distance between location and destination = 66 × 2 = 132

∴ Distance travelled by Kantesh to complete the journey

⇒ {132/(4x/5 + S)} + {132/(4x/5 – S)} = t₁

where S → Speed of current

Distance travelled by Sudesh to complete the journey

⇒ {132/(x + S)} + {132/(x – S)} = t₂

Statement II alone is not sufficient to answer the question

 

Using statement I and statement II together

Speed of Sudesh = 35 km/hr, Speed of Kantesh = (4/5) × 35 = 28 km/hr

Total distance travelled = 132 km/hr

Distance travelled by Kantesh to complete the journey

⇒ {132/(28 + 5)} + {132/(28 – 5)} = 4 + 5.739 = 9.739 ≈ 9.74 hr

Distance travelled by Kantesh to complete the journey

⇒ {132/(35 + 5)} + {132/(35 – 5)} = 3,3 + 4.4 = 7.7 hr

∴ Difference in time = 9.74 – 7.7 = 2.04 hrs

∴ The data in both statements I and II together are needed to answer the question.