Tag: maths

Questions Related to maths

Three geometric means between 5 and 3125 are___.

mean and median mean maths assumed mean method assumed mean method of finding mean measure of central tendency

  1. 15,75,375

  2. 25,125,625

  3. 11,44,176

  4. 10,40,160

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Correct Option: B
Explanation:

The geometric mean is a geometric series which is in the form of arn where a is the first term and r is the common ratio.

T1= 5 and T5 = 3125

Now, T1/T5 = 5/ 3125

=>ar1//ar5 =1/ 625

=> 1/ r4 = 1/625

=> r4 = 625

=> r = 5

So if r=5, then a= 1

T2 = ar2

      = 1(5) 2 = 25

T3 = ar3

      = 1(5) 3 = 125

T4 = ar4

      = 1(5)4 = 625

Therefore, three geometric means between 5 and 3125 are 25, 125 and 625. 

The most appropriate average to be used to compute the average rate of growth in population is:

mean and median mean maths assumed mean method assumed mean method of finding mean measure of central tendency

  1. Arithmetic mean

  2. Median

  3. Geometric mean

  4. Harmonic mean

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Correct Option: C
Explanation:

In geometric mean method, the average percentage increase in the population is assumed to be constant decade to decade through which future population is worked out. Therefore, it is the most appropriate average to be used to compute the average rate of growth in population. 

The mean of a sample of size $10$ is $15$. If the value of each item is reduced by $2$, the mean of the sample will be_____.

mean and median mean maths assumed mean method assumed mean method of finding mean measure of central tendency

  1. $15$

  2. $13$

  3. $11$

  4. $22$

Show answer
Correct Option: B
Explanation:

Mean refers to the average amount in a given group of data. So arithmetic mean can be calculated by adding the first term and the last term of the series and then dividing the sum by 2. In the given series the first term 'a' is decreased by 2 and  the last term 'b' is also decreased by 2 , so the 

Mean = {(a-2)+ (b-2)}  /2 

          = (a+b-4) /2 

          = {(a+b)/2} - 4/2

          = {(a+b)/2} - 2 

Therefore, the mean is also decreased by 2. So,if the mean was 15 then now it will be 13. 

If the average weight of $150$ students is $60$ kg., what will be the number of boys and girls in the school if the average weight of boys and girls is $70$kg and $55$kg. respectively?

mean and median mean maths assumed mean method assumed mean method of finding mean measure of central tendency

  1. $(50,100)$

  2. $(100,50)$

  3. $(40,110)$

  4. $(90,60)$

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Correct Option: A

Harmonic mean is a part of _______________.

mean and median mean maths assumed mean method assumed mean method of finding mean measure of central tendency

  1. Positional average

  2. Mathematical average

  3. Both a & b

  4. None of the above

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Correct Option: B
Explanation:

Mathematical average refers to all such average where a figure is taken out through mathematical methods from the a given series that represents the whole series. Harmonic mean is a mathematical tool which is used to calculate average of a certain series. Therefore, it is a part of mathematical average. 

6 dozen eggs are bought for Rs. 48. How much will 132 eggs cost ?

introduction to ratio and percentages comparing quantities maths

  1. Rs. 78

  2. Rs. 80

  3. Rs. 82

  4. Rs. 88

Show answer
Correct Option: D
Explanation:

6 dozen eggs = 72 eggs
Let the required amount be Rs. x.

Now,
$72:132::48:x$
$\dfrac{72}{132}=\dfrac{48}{x}$

$x=88$
Therefore,
Required amount = $Rs. 88$

The food stocks in a hostel are sufficient for 1200 students for 20 days . If 400 more students joined the hostel , the stocks just for ... days .

introduction to ratio and percentages comparing quantities maths

  1. 12

  2. 15

  3. 18

  4. 21

Show answer
Correct Option: B
Explanation:

Let food stock is sufficient for $x$ days.

Given,
$M _{1}=1200$
$D _{1}=20$
$M _{2}=1200+400=1600$
$D _{2}=x$
Then, using $M _{1}D _{1}=M _{2}D _{2}$
$1200\times 20 = 1600\times x$
$x=\dfrac{1200\times 20}{1600}$
$x=15$
Therefore, now the food stock is sufficient for $15$ days.

The time taken (in hours) by a car to travel $900km$ if it travels $600 km $ in $12 hrs$.

introduction to ratio and percentages comparing quantities maths

  1. 18

  2. 16

  3. 15

  4. None of these

Show answer
Correct Option: A
Explanation:

Time taken to cover $600km$ is `12 Hrs

Speed of car is given as $\dfrac{600}{12}=50kmph$
Time taken to cover $900km$ is $\dfrac{900}{50}=18hrs$

If 10% of x=20% of y, then $x:y$ is equal to

introduction to ratio and percentages comparing quantities maths

  1. $1:2$

  2. $2:1$

  3. $5:1$

  4. $10:1$

Show answer
Correct Option: B
Explanation:
Given,

$10$% $x$ = $20$% $y$

$\dfrac{x}{y}=\dfrac{20}{10}$%

$\therefore x:y=2:1$

$33\dfrac { 1 }{ 3 } %\quad of\quad 1\dfrac { 1 }{ 2 } $ minute is equal to ___

introduction to ratio and percentages comparing quantities maths

  1. 2000 seconds

  2. 5000 seconds

  3. 3000 seconds

  4. 6000 seconds

Show answer
Correct Option: A
Explanation:
$1$minute$=60$seconds
$33\dfrac{1}{3}$ minutes$=33\dfrac{1}{3}\times 60$ seconds
$=\dfrac{100}{3}\times 60$ seconds
$=100\times 20$ seconds
$=2000$seconds.