Tag: index numbers

Quizzes (2) Questions (70)

Questions Related to index numbers

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

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

For consumer price index, price quotations are collected from:

  1. Fair price shops

  2. Government depots

  3. Retailers

  4. Whole-sale dealers
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\Rightarrow$  For consumer price index, price quatations are collected from: $Retailers.$

$\Rightarrow$   A retailer is a company that buys products from a manufacturer or wholesaler and sells them to end users or customers. In a sense, a retailer is an intermediary or middleman that customers use to get products from the manufacturers.
$\Rightarrow$  Retailers are experts in marketing, sales, merchandise inventory, and knowing their customers. They purchase the goods from the manufacturers at cost and market them to consumers at retail prices. 
$\Rightarrow$  The retail price can be anywhere from 10 percent to 50 percent higher than the manufacturer cost. 

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

When the prices of rice are to be compared, we compute: 

  1. Volume index

  2. Value index

  3. Price index

  4. Aggregative index
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\Rightarrow$  When the prices of rice are to be compared, we compute: $Price\,Index.$

$\Rightarrow$  Price index, measure of relative price changes, consisting of a series of numbers arranged so that a comparison between the values for any two periods or places will show the average change in prices between periods or the average difference in prices between places. 
$\Rightarrow$  In most countries price indexes are used to measure inflation, each focusing on the prices of a collection of goods and services important to a particular segment of the economy.

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

Price relatives computed by chain base method are called: 

  1. Price relatives

  2. Chain indices

  3. Link relatives

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

$\Rightarrow$  Price relatives computed by chain base method are called $Link\,\,relatives.$

$\Rightarrow$  Under this method, the base year’s price does not remain fixed but moves step from year to year. In other words, the immediately preceding year’s price becomes the base year’s price for each of the succeeding years.
$\Rightarrow$  Under this method, the base year’s price does not remain fixed but moves step from year to year. In other words, the immediately preceding year’s price becomes the base year’s price for each of the succeeding years.

$\Rightarrow$  $Chain\, index$ = $\dfrac{Average\, link\, relative\, of\, current\, year \times Chain\, index\, of\, previous\, year}{100}$