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TANCET 2022 Solved Papers

Question Numbers: 61-80

PART - IV

DIRECTIONS: Data sufficiency problems consist of a question and two statements, labelled (I) and (II), in which certain data are given. You have to decide whether the data given in the statements is sufficient for answering the question. Use the data given, plus your knowledge of mathematics and every day facts, to mark your answer as:

a. If the question can be answered with the help of statement I alone,

b. If the question can be answered with the help of statement II alone,

c. If both, statement I and statement II are needed to answer the question, and

d. If the question cannot be answered even with the help of both the statements.

Question : 70 of 100

Marks: +1, -0

Two cars pass each other in opposite direction. How long would they take to be 500 km apart?

I. The sum of their speeds is

135 \mathrm{~km} / \mathrm{hr}

II. The difference of their speed is

25 \mathrm{~km} / \mathrm{hr}

If the question can be answered with the help of statement I alone,
If the question can be answered with the help of statement II alone,
If both, statement I and statement II are needed to answer the question, and
If the question cannot be answered even with the help of both the statements.

Validate

Solution:

Concept:

When two objects move in opposite directions, their relative speed equals the sum of their individual speeds.

Explanation:

The time required to become

500

km apart is found by dividing the distance by the relative speed.

So, time

= \frac{500}{\text{relative speed}}

For opposite directions, relative speed

= v_1 + v_2

Statement I gives

v_1 + v_2 = 135

km/hr, which is exactly the relative speed.

Thus, time

= \frac{500}{135}

hours, so statement I alone is sufficient.

Statement II gives only

v_1 - v_2 = 25

km/hr.

This difference is not the relative speed when the cars move in opposite directions.

Therefore, statement II alone is not sufficient to find the required time.

Answer:

Statement I alone is sufficient. Option A.

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