TANCET 2014 DS 79: Rates

What should we know from the Question Stem?

Before evaluating the two statements, answer the following questions to get clarity on when the data is sufficient.

What kind of an answer will the question fetch?

The question is "How fast is Automobile A travelling?"

The answer to the question should be the speed of Automobile A, a number followed by a unit of speed.

When is the data sufficient?

If we are able to come up with a UNIQUE value for the speed of Automobile A, the data is sufficient.

If we are not able to come up with a unique value – either we cannot find an answer with the data in the statement(s) or if we find more than one value, the data is NOT sufficient.

What data is available from the question stem?

Automobile A is travelling at \\frac{2}{3}\\)^rd the speed of Automobile B.

Statement (1) ALONE

If both automobiles increased their speed by 10 km per hour, Automobile A would be travelling at \\frac{3}{4}\\)^th the speed of Automobile B.

Let the speed of Automobile B be ‘b’ kmph.

So, speed of Automobile A = \\frac{2}{3}\\)b.

If each increased its speed by 10 kmph, the speeds of A and B will be (\\frac{2}{3}\\)b + 10) and (b + 10) respectively.

From statement 1, (\\frac{2}{3}\\)b + 10) = \\frac{3}{4}\\)(b + 10)

\\frac{3}{4}\\)b – \\frac{2}{3}\\)b = 10 – 7.5

Solving the equation, we get b = 30 kmph.

So, speed of Automobile A = 20 kmph

We are able to find a UNIQUE value for the speed of Automobile A using data in statement 1.

  Statement (1) ALONE is sufficient.

The moment we realize that statement (1) ALONE is sufficient, we can narrow down our choices to 1 or 4

To determine whether the answer is choice 1 or choice 4, we need to evaluate statement (2). Remember that you have to evaluate statement (2) even if statement (1) is sufficient.

Statement (2) ALONE

If both automobiles decreased their speed by 10 km per hour, Automobile A would be travelling at \\frac{1}{2}\\) the speed of Automobile B.

Remember: When you are evaluating statement (2) ALONE, please do not recall information that you read in statement (1). Anything said about the speeds of either automobile A or B in statement (1) should not be used while evaluating statement (2).

We know a = \\frac{2}{3}\\)b from the question stem.

If each decreased its speed by 10 kmph, the speeds of A and B will be (\\frac{2}{3}\\)b – 10) and (b – 10) respectively.

From statement 2, (\\frac{2}{3}\\)b – 10) = \\frac{1}{2}\\) (b – 10)

\\frac{2}{3}\\)b – \\frac{1}{2}\\)b = 10 – 5

Solving the equation, we get b = 30 kmph.

So, speed of Automobile A = 20 kmph.

Using statement (2) ALONE we could get a UNIQUE answer.

  Statement (2) ALONE is ALSO sufficient.

Each statement is INDEPENDENTLY sufficient, we can eliminate choice 1.

  Hence, choice (4) is the answer.