Speed Distance Time : TANCET Quant

Speed Distance Time is one of the topics from which you should expect a question either in the quantitative reasoning section or in the data sufficiency section of the TANCET MBA.

Here is a relatively easy quantitative reasoning question from this topic

Question

It takes Kiran 50 minutes lesser to cover a distance if she travels three times as fast as she does now. How long will she take to cover the distance if she travels twice as fast as she does now?
1. 50 minutes
2. 75 minutes
3. 150 minutes
4. 100 minutes
5. 37.5 minutes

Correct Answer : Choice 5. 37.5 minutes

Explanatory Answer

Let Kiran's present speed be S km/min. And let her take t minutes to reach her destination.

If Kiran travels three times as fast as she does now i.e., at 3S, she will cover the same distance in 1/3 of the time i.e., in t/3 minutes.

So, she is saving (t - t/3) minutes = 2t/3 minutes.
The question states that she is saving 50 minutes.
Therefore, 2t/3 = 50
or t = 75 minutes.

If she travels at S km/min, she will reach her destination in 75 minutes.

So, if she travels at 2S km/min, she will take half that time = 75/2 minutes = 37.5 minutes.

TANCET Quant : Linear Equations, Word Problems

Here is a word problem that requires you to frame a pair of linear equations, solve the equations to arrive at an answer.

Rajesh is 10 years younger to Baskar. 10 years back, Rajesh's age was two-thirds that of Baskar's. How old is Baskar now?
1. 30
2. 40
3. 20
4. 16
5. 28

Correct Answer is Choice (2). 40 years.

Explanatory Answer

Let the present age of Baskar be 'b' and that of Rajesh be 'r'.
So, r = b - 10 .... eqn (1).

10 years back Rajesh was (r - 10) years old. 10 years back Baskar was (b - 10) years old.
The question states that 10 years back Rajesh was two thirds as old as Baskar was.

i.e., (r - 10) = (2/3)*(b - 10) .... eqn (2).
Cross multiplying, we get 3(r - 10) = 2(b - 10)
or 3r - 30 = 2b - 20 .... eqn (2)

From eqn (1) we can substitute r as (b - 10) in eqn (2)
So, 3(b - 10) - 30 = 2b - 20
or 3b - 30 - 30 = 2b - 20
or b = 40.

The present age of Baskar is 40 years.

Word problems : Linear Equations

You should anticipate a question that expects you to convert information presented in words into an equation and solve it.

They are commonly referred to as "word problems". The key to getting those questions right is to try and decode the information in the sentence and frame equations accordingly.

Here is a question that will give you an idea of how to frame a linear equation from the information given in the question statement.

If the result of seven more than four times a number is tripled, the resultant number is three more than fifteen times the number. What is the number?
1. 6
2. 7
3. 4
4. 15
5. 12

TANCET Math prep question - Linear Equations

Linear Equations is one of the fundamental topics from which you could expect one or two questions in the TANCET test.

A Linear Equation is one in which the power or the exponent of the variable is 1. An equation of the form 3x + 2y = 17 is a linear equation.

A linear equation in two variables x and y represents a straight line when plotted on a x - y plane. The equation of the x-axis is y = 0 and that of the y-axis is x = 0.

The following question is a word problem in linear equation. You will be presented some information as a statement and you will be expected to fram linear equation based on the information provided there and solve the linear equation to get the answer.

Question
QuestionRam's father is thrice as old as Ram. 6 years hence, his father will be 24 years older than Ram. How old is Ram?
1. 24 years
2. 18 years
3. 12 years
4. 36 years
5. 42 years

Correct Answer and Explanation
Let Ram's present age be R.
So, his father's present age is 3R.

6 years hence, Ram will be (R + 6) years old
6 years hence, Ram's father will be 3R + 6 years old.
The question states that 6 years hence, Ram's father is 24 years older than Ram.
i.e., 3R + 6 = (R + 6) + 24

Or 3R + 6 = R + 30
or 2R = 24 or R = 12.
Ram's present age is therefore 12 years.

Shortcut Approach
You should actually solve this question by going back from the answer choices. That way, you will save a lot of time. Anyone who is serious about cracking the TANCET should commence your preparation for the TANCET exam not later than the day your fifth semester exams are over if you are in a 3-year degree program or after your seventh semester exam gets over if you are in a 4-year degree program.