Tag: business mathematics and statistics

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Questions Related to business mathematics and statistics

Multiple choice business mathematics and statistics introduction to index number introduction to index numbers index numbers applied statistics

When the price of a year is. divided by the price of a particular year we get:

  1. Simple relative

  2. Link relative

  3. (a) and (b) both

  4. None of them
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\Rightarrow$  When the price of year is divided by the price of particular year we get : $Simple\,\,relative.$

$\Rightarrow$  Under this method, the price Index for a given year is calculated as the simple average of the price relatives of the different items included in the index numbers. 
$\Rightarrow$  The simple average used, here, may be of any type viz. arithmetic mean, geometric mean, harmonic mean, median or mode, but arithmetic mean is usually preferred to, for its simplicity in calculation and geometric mean for its ability of measuring the relative changes which is the inherent feature of an index number.

Multiple choice business mathematics and statistics introduction to index number introduction to index numbers index numbers applied statistics

When the price of a divided by the price of the preceding year, we, get:

  1. Value index

  2. Link relative

  3. Simple relative

  4. None of them
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\Rightarrow$  When the price of divided by the price of the preceding year, we get : $Link\,\,relative.$

$\Rightarrow$  This method is based on the assumption that the trend is linear and cyclical variations are of uniform pattern. 
$\Rightarrow$  The link relatives are percentages of the current period (quarter or month) as compared with the previous period. With the computations of the link relatives and their average, the effect of cyclical and the random components is minimized. Further, the trend gets eliminated in the process of adjustment of chain relatives
$\Rightarrow$  This method is less complicated than the ratio to moving average and the ratio to trend methods.However, this method is based upon the assumption of a linear trend which may not always hold true.

Multiple choice business mathematics and statistics introduction to index number introduction to index numbers index numbers applied statistics

If the price of potatoes is reduced by $25\%$, one can buy $6.25$ kg more for Rs. $100$. The reduced price of potatoes is  

  1. Rs. $3$/- per kg
  2. Rs. $3.50$ per kg
  3. Rs. $4$/- per kg
  4. Rs. $4.50$ per kg
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let original price per kg $=x$.

Reduction $=25$%
$\therefore $  New price per kg $=x\left( 1-\dfrac { 25 }{ 100 }  \right) $
                                   $=\dfrac { 3x }{ 4 } $
Now, for $Rs100$, let customer buy $'y'$ kg of potatoes.
$\therefore \quad 100=$ (initial price per kg) $\times $ (weight bought)
$\Rightarrow \quad 100=xy\quad \longrightarrow (i)$
For the reduced cost,
$100=$ (new price per kg) $\times $ (weight bought)
$\Rightarrow \quad 100=\left( \dfrac { 3x }{ 4 }  \right) \left( y+6.25 \right) $
But from eq $(i)$   $100=xy$
$\therefore \quad xy=\dfrac { 3x }{ 4 } \left( y+6.25 \right) $
$\Rightarrow \quad 4y=3y+18.75$
$\Rightarrow \quad y=18.75$
$\therefore \quad x=\dfrac { 100 }{ 18.75 } =\dfrac { 100\times 100 }{ 1875 } $
$\therefore $  Reduced price $=\dfrac { 3x }{ 4 } =\dfrac { 3 }{ 4 } \times \dfrac { 100\times 100 }{ 1875 } $  per kg
                              $=4$  per kg

Multiple choice business mathematics and statistics introduction to index number introduction to index numbers index numbers applied statistics

Fisher's Ideal Formula satisfies __________ test.

  1. Both B & C

  2. Factor Reversal Test

  3. Time Reversal Test

  4. None of above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Fisher's Ideal Formula refers to the geometric mean of Laspeyres and Paasche formula. It is also known as Ideal formula also. It satisfies Factor Reversal Test as well as Time Reversal Test.

Multiple choice business mathematics and statistics introduction to index number introduction to index numbers index numbers applied statistics

The chain base indices are not suitable for:

  1. Long range comparisons

  2. Short range comparisons

  3. Percentages

  4. Ratios
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\Rightarrow$  The chain base indices are not suitable for : $Long\,range\,comparisons.$

$\Rightarrow$  In chain base method method, there is no fixed base period.
$\Rightarrow$  The chief advantage of this method is that the price relatives of a year can be compared with the price levels of the immediately preceding year. Businesses mostly interested in comparing this time period rather than comparing rates related to the distant past will utilize this method.

$\Rightarrow$  Another advantage of the chain base method is that it is possible to include new items in an index number or to delete old times which are no longer important. But the chain base method has the drawback that comparisons cannot be made over a long period.

Multiple choice business mathematics and statistics introduction to index number introduction to index numbers index numbers applied statistics

In chain base method, the base period is:

  1. Fixed

  2. Not fixed

  3. Constant

  4. Zero
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\Rightarrow$  In chain base method, the base period is : $Not\,fixed.$

$\Rightarrow$  In this method, there is no fixed base period; the year immediately preceding the one for which the price index has to be calculated is assumed as the base year. 
$\Rightarrow$  Thus, for the year 1994 the base year would be 1993, for 1993 it would be 1992, for 1992 it would be 1991, and so on. In this way there is no fixed base and it keeps on changing.
$\Rightarrow$  advantage of the chain base method is that it is possible to include new items in an index number or to delete old times which are no longer important. 

Multiple choice business mathematics and statistics introduction to index number introduction to index numbers index numbers applied statistics

Two hundred items were sold at a snack stand for a total of $Rs$. $130.00$. The only items sold were cansof pop for $Rs$. $0.50$ and bags of popcorn for $Rs$. $0.75$. How many of each item were sold?

  1. $120$ cans of pop, $80$ bags of popcorn
  2. $80$ cans of pop, $120$ bags of popcorn
  3. $160$ cans of pop, $40$ bags of popcorn
  4. $40$ cans of pop, $160$ bags of popcorn
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

  Let us assume no of cans of pop sold =x
no of bags of pop sold=200-x
So, as per question,
$0.50*x+0.75(200-x)=130$
$0.50x+150-0.75x=130$
$0.25x=20$
$x=80$
So, no of bags of pop sold=200-x=200-80=120
Answer (B) 80 cans of pop, 120 bags of popcorn