Arithmetic aptitude :: Time and Distance :: Data Sufficiency 1

• Time and Distance - General Questions
• Time and Distance - Data Sufficiency 1
• Time and Distance - Important Formulas and Facts

1. Speed $=\left(\frac{Distance}{Time}\right)$, Time $=\left(\frac{Distance}{Speed}\right)$, Distiance $=(Speed\times Time)$

2. $x$ km/hr $=\left(x\times\frac{5}{18}\right)$ m/sec

3. $x$ m/sec $=\left(x\times\frac{18}{5}\right)$

4. If speed ratios of X and Y is $x:y$, then the time ratio by them to cover same distance $=\frac{1}{x}:\frac{1}{y}$ or $y:x$

5. Suppose an object covers a certain distance at $x$ km/hr and an equal distance at $y$ km/hr. Then, the average speed of during the

whole travel is $\left(\frac{2xy}{x+y}\right)$ km/hr.

The cities X, Y and Z are on a straight line. City Z is between X and Y. The distance from X to Y is $100$ km. How far is X from Z ?

I. The distance from X to Y is $25\%$ more than the distance from Z to Y.

II. The distance from X to Z is $\frac{1}{4}$ of the distance Z to Y

Answer:

Explanation:

.______.___________.
X   x    Z  (100 - x) Y

Let $XZ$ = $x$ km. Then, $ZY$ $=(100-x)$ km.

I. $XY-125\%$ of $ZY$

$\Leftrightarrow$ $100=\frac{125}{100}\times(100-x)$

$\Leftrightarrow 100-x$ $=\frac{100\times 100}{125}$ $=80$.

$\Leftrightarrow x=20$ km.

$\therefore XZ=20$ km.

Thus, I alone gives the answer.

II. $XZ=\frac{1}{4}ZY$

$\Leftrightarrow x=$ $\frac{1}{4}(100-x)$

$\Leftrightarrow$ $5x=100$ $\Leftrightarrow x=20$.

$\therefore XZ=20$ km.

Thus, II alone gives the answer.

$\therefore$ Correct answer is (C).

A car and a bus start from the town X at the same time. How far is the town Y from the town X ?

I. The car travelling at an average speed of 40 km/hr reaches town Y at 4:35 pm.

II. Th bus reaches town Y at 6:15 pm, at an average speed of 60 km/hr.

Answer:

Explanation:

Let XY = $x$ km. From I and II, we get :

$\frac{x}{40}-\frac{x}{60}$ $=1\frac{40}{60}$ [(6:15 pm) - (4:35 pm) = 1 hr 40 min]

$\Leftrightarrow$ $\frac{x}{40}-\frac{x}{60}=\frac{100}{60}$.

This gives $x$.

$\therefore$ Correct answer is (E).

What is the average speed of the car over the entire distance ?

I. The car covers the whole distance in four equal stretches at speeds of 10 kmph, 20 kmph, 30 kmph and 60 kmph respectively.

II. The total time taken is 36 minutes.

Answer:

Explanation:

Let the whole distance be $4x$ km.

I. Total time taken $=\left(\frac{x}{10}+\frac{x}{20}+\frac{x}{30}+\frac{x}{60}\right)$

$=\frac{(6x+3x+2x+x)}{60}$

$=\frac{12x}{60}$ $=\frac{x}{5}$.

$\therefore$ Speed $=\frac{Distance}{Time}$ $=\frac{4x}{\left(\frac{x}{5}\right)}$ kmph = 20 km/hr.

$\therefore$ I alone is sufficient to answer the question.

II. alone does not give the answer.

What is the usual speed of the train ?

I. The speed of the train is increased by 35 km/hr to reach the destination 150 km away in time.

II. The train is late by 30 minutes.

Answer:

Explanation:

Let the usual speed of the train be $x$ kmph.

Time taken to cover 150 km at usual speed $=\frac{150}{x}$ hrs.

I. Time taken at increased speed $=\frac{150}{x+25}$ hrs.

II. $\frac{150}{x}-\frac{150}{(x+25)}$ $=\frac{30}{60}$.

$\Leftrightarrow$ $\frac{1}{x}-\frac{1}{(x+25)}$ $=\frac{1}{300}$

$\Leftrightarrow$ $\left[(x+25)-x\right]\times 3000$ $=x(x+25)$

$\Leftrightarrow$ $x^{2}+25x-7500=0$

$\Leftrightarrow$ $(x+100)(x-75)=0$

$\Leftrightarrow x=75$.

Thus, I and II together give the answer.

$\therefore$ Correct answer is (E).

• Time and Distance - General Questions
• Time and Distance - Data Sufficiency 1