Quantitative Aptitude

Averages

1,527 Questions
All Basic average and reverse calculation 405 Adding or removing an observation 342 Weighted and combined averages 320 Replacement and correction of a recorded value 233 Ratio shortcut for two-group mixtures 111 Equal-distance average speed 59 Age, score, weight, and spending applications 32 Consecutive terms and arithmetic progressions 25

Averages Questions

Multiple choice

In Roscher's class, a student with an average score from $80$ to $89$, inclusive, gets a $B$ grade. His grade is based only on $3$ tests. The highest possible score on each of these tests is $100$ points. Roscher scored $79$ points in his first test and $95$ in his second test. If $y$ represents his score in the third test, determine which of the following inequalities below shows all values of $y$ that would earn Roscher a $B$ in his Physics class.
  1. $\displaystyle 66\le y\le 93$
  2. $\displaystyle 66\le y\le 100$
  3. $\displaystyle 80\le y\le 89$
  4. $\displaystyle 80\le y\le 93$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Average score = (79 + 95 + y) / 3. For a B grade, 80 <= (174 + y) / 3 <= 89. 240 <= 174 + y <= 267. 66 <= y <= 93.

Multiple choice

In a class, in an examination in Mathematics, $10$ students scored $100$ marks each, $2$ students scored zero and the average of the remaining students is $72$ marks. If the class average is $76$, then the number of students in the class is
  1. $44$
  2. $40$
  3. $38$
  4. $34$
  5. $32$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let N be the total number of students. 10 students scored 100 (sum=1000). 2 students scored 0 (sum=0). Remaining (N-12) students average 72 (sum=72(N-12)). Total sum = 1000 + 72(N-12) = 76N. 1000 + 72N - 864 = 76N. 136 = 4N. N = 34.

Multiple choice

In a Mathematics test, the average marks of boys is $x\%$ and the average marks of girls is $y\%$ with $x\neq y$. If te average marks of all students is $z\%$ the ratio of the number of girls to the total number of students is?
  1. $\displaystyle\frac{z-x}{y-x}$
  2. $\displaystyle\frac{z-y}{y-x}$
  3. $\displaystyle\frac{z+y}{y-x}$
  4. $\displaystyle\frac{z+x}{y-x}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let B be the number of boys and G be the number of girls. Total students = B + G. The weighted average is (Bx + Gy) / (B + G) = z. Rearranging: Bx + Gy = zB + zG, so B(x - z) = G(z - y). Thus, G/B = (x - z) / (z - y) = (z - x) / (y - z). The ratio of girls to total students is G / (B + G) = (z - x) / (y - x).

Multiple choice

$A$ person goes from point $A$ to point $B$ with speed $V_{1}$ and comes back to point $A$ from point $B$ with speed $V_{2}$. Its average speed and average velocity respectively are
  1. $0,\ 0$
  2. $\dfrac{V_{1}+V_{2}}{2}\ ,\ 0$
  3. $\dfrac{V_{1}+V_{2}}{4}\ ,\ 0$
  4. $\dfrac{2V_{1}V_{2}}{V_{1}+V_{2}}, \ 0$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Average speed is total distance divided by total time, which for a round trip is 2V1V2 / (V1+V2). Average velocity is displacement divided by time; since the person returns to the starting point, displacement is 0.

Multiple choice

A passenger travels along the straight road for half the distance with velocity, ${ v }{ 1 }$ and the remaining half distance with velocity, ${ v }{ 2 }$. Then average velocity is given by
  1. ${ v }_{ 1 }{ v }_{ 2 }$
  2. $\dfrac{v_2^2 }{ v _1^2}$
  3. $\dfrac{{ \left( { v }_{ 1 }+{ v }_{ 2 } \right) }}{2}$
  4. $\dfrac{2{ v }_{ 1 }{ v }_{ 2 }}{{ \left( { v }_{ 1 }+{ v }_{ 2 } \right) }}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Average velocity is total displacement divided by total time. If distance is d, total distance is 2d. Time taken is d/v1 + d/v2. Average velocity = 2d / (d/v1 + d/v2) = 2 / (1/v1 + 1/v2) = 2v1v2 / (v1 + v2).

Multiple choice

A boy goes to school from his home at a speed of $x$ km/hr. and comes back at a speed of $y$ km/hr. then the average speed of the boy is
  1. $\displaystyle \frac{x+y}{2}km/hr$
  2. $\displaystyle \sqrt{xy}km/hr$
  3. $\displaystyle \frac{2xy}{x+y}km/hr$
  4. $\displaystyle \frac{x+y}{2xy}km/hr$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Average speed = Total distance / Total time. Let distance be d. Time taken to go = d/x. Time taken to return = d/y. Total time = d/x + d/y = d(x+y)/(xy). Average speed = 2d / (d(x+y)/(xy)) = 2xy / (x+y).

Multiple choice

A person pedals from his house to his office at a speed of $x_1$ km/hour and returns by the same route at a speed of $x_2$ km/hour. What is his average speed ?
  1. $ \displaystyle \frac {x_1x_2}{2x_1 - x_2}$
  2. $ \displaystyle \frac {x_1x_2}{x_1 + x_2}$
  3. $ \displaystyle \frac {2x_1x_2}{x_1 + x_2}$
  4. $ \displaystyle \frac {x_1x_2}{2x_1 + x_2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Average speed is total distance divided by total time. If distance is D, time taken is D/x1 + D/x2. Average speed = 2D / (D/x1 + D/x2) = 2x1x2 / (x1 + x2).

Multiple choice

A body traversed half of the distance with a velocity $V_0$. The remaining part $V_1$ for half of the time and with the velocity $V_2$ for the other half of the time. Find the average velocity of the body over the whole journey.
  1. $\dfrac{2V_0(V_1 + V_2)}{(2V_0 + V_1 + V_2)}$
  2. $\dfrac{3V_0(V_1 + V_2)}{(2V_0 + V_1 + V_2)}$
  3. $\dfrac{2V_0(V_1 + V_2)}{(3V_0 + V_1 + V_2)}$
  4. $\dfrac{V_0(V_1 + V_2)}{(2V_0 + V_1 + V_2)}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let total distance be 2d. Time for first half is d/V0. For the second half, time is t. Distance covered is (V1*t/2) + (V2*t/2) = d. So t = 2d/(V1+V2). Total time = d/V0 + 2d/(V1+V2) = d(V1+V2+2V0)/(V0(V1+V2)). Average velocity = 2d / total time = 2V0(V1+V2)/(2V0+V1+V2).

Multiple choice

Emily takes a trip, driving with a constant velocity of $90$ $km/h$ to the north except for a $30$ min rest stop. If Emily's average velocity is $75$ $km/h$ to the north, what is the total distance travelled? (in km)
  1. $124$
  2. $225$
  3. $150$
  4. $280$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let d be the total distance. Total time taken = (d / 90) + 0.5 hours. Average velocity = Total distance / Total time, so 75 = d / (d/90 + 0.5). Thus, 75(d/90 + 0.5) = d, which simplifies to (5/6)d + 37.5 = d. Then (1/6)d = 37.5, so d = 225 km.