Tag: business mathematics and statistics

Questions Related to business mathematics and statistics

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

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

  1. Simple relative

  2. Link relative

  3. (a) and (b) both

  4. None of them

Show answer
Correct Option: A
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.

The current price of a soap is Rs 10.  The base price is 4. Find price relative.

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

  1. 0.4

  2. 0.25

  3. 0.30

  4. None of the above

Show answer
Correct Option: B
Explanation:

Price relative $=$ Base Price $/$ Current Price

                       $=\dfrac{4}{10} = 0.25$

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

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

  1. Value index

  2. Link relative

  3. Simple relative

  4. None of them

Show answer
Correct Option: B
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.

Cost of living at two different cities can be compared with the help of

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

  1. Value index

  2. Consumer price index

  3. Volume index

  4. Un-weighted index

Show answer
Correct Option: B
Explanation:

Consumer Price Index can be used to compare the cost of living at two different cities.

More the CPI, higher is the cost of living in that city.

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  

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

  1. Rs. $3$/- per kg

  2. Rs. $3.50$ per kg

  3. Rs. $4$/- per kg

  4. Rs. $4.50$ per kg

Show answer
Correct Option: C
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

Fisher's Ideal Formula satisfies __________ test.

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

  1. Both B & C

  2. Factor Reversal Test

  3. Time Reversal Test

  4. None of above

Show answer
Correct Option: A
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.

Indices calculated by the chain base method are free from:

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

  1. Seasonal variations

  2. Errors

  3. Percentages

  4. Ratios

Show answer
Correct Option: A
Explanation:

Indices calculated by chain base method are free from seasonal variations.

The chain base indices are not suitable for:

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

  1. Long range comparisons

  2. Short range comparisons

  3. Percentages

  4. Ratios

Show answer
Correct Option: A
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.

In chain base method, the base period is:

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

  1. Fixed

  2. Not fixed

  3. Constant

  4. Zero

Show answer
Correct Option: B
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. 

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?

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

  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

Show answer
Correct Option: B
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