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In 1976 the average price of a commodity was 20% more than that in 1975 but 20% less than that in 1974 and more over it was 50% more than that in 1977. The price relatives using 1975 as base year (1975 price relative = 100) then the reduce date is :
- a)8,.75
- b)150,80
- c)75,125
- d)None of these.
Correct answer is option 'B'. Can you explain this answer?
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In 1976 the average price of a commodity was 20% more than that in 197...
Given information:
- Average price of commodity in 1976 was 20% more than that in 1975.
- Average price of commodity in 1976 was 20% less than that in 1974.
- Average price of commodity in 1976 was 50% more than that in 1977.
To find: Price relatives using 1975 as base year.
Solution:
Let the average price of the commodity in 1974 be x.
Then, the price of the commodity in 1976 is 0.8x (20% less than that in 1974).
Also, the price of the commodity in 1975 is (5/6)*(0.8x) = (4/6)*x = (2/3)*x (20% more than that in 1974).
Therefore, the price relatives for 1975 and 1974 are:
- Price relative for 1975 = (2/3)x/x * 100 = 66.67
- Price relative for 1974 = x/x * 100 = 100
Now, let the price of the commodity in 1977 be y.
Then, the price of the commodity in 1976 is 1.5y (50% more than that in 1977).
Also, the price of the commodity in 1975 is (4/5)*(1.5y) = (6/5)*y.
Therefore, the price relative for 1977 is:
- Price relative for 1977 = y/x * 100
To find the reduce date, we need to find the year in which the price relative is less than 100 (i.e. when the price of the commodity decreased compared to the base year 1975).
Let the reduce date be z.
Then, the price of the commodity in year z is (4/5)*(1.5y) = (6/5)*y.
Therefore, the price relative for year z is:
- Price relative for year z = (6/5)*y/x * 100
Since the price relative for year z is less than 100, we have:
(6/5)*y/x * 100 < />
=> (6/5)*y/x < />
=> y/x < />
Substituting the value of y/x from the price relatives for 1975 and 1977, we get:
(6/5)*y/x = (6/5)*(y/x) * (66.67/100) * (100/y)
=> (6/5)*(y/x) * (2/3) < />
=> (y/x) < />
Therefore, the reduce date is the year in which the price of the commodity was less than 83.33% of the price in 1974.
From the given options, the only year that satisfies this condition is option B: 150,80.
- Average price of commodity in 1976 was 20% more than that in 1975.
- Average price of commodity in 1976 was 20% less than that in 1974.
- Average price of commodity in 1976 was 50% more than that in 1977.
To find: Price relatives using 1975 as base year.
Solution:
Let the average price of the commodity in 1974 be x.
Then, the price of the commodity in 1976 is 0.8x (20% less than that in 1974).
Also, the price of the commodity in 1975 is (5/6)*(0.8x) = (4/6)*x = (2/3)*x (20% more than that in 1974).
Therefore, the price relatives for 1975 and 1974 are:
- Price relative for 1975 = (2/3)x/x * 100 = 66.67
- Price relative for 1974 = x/x * 100 = 100
Now, let the price of the commodity in 1977 be y.
Then, the price of the commodity in 1976 is 1.5y (50% more than that in 1977).
Also, the price of the commodity in 1975 is (4/5)*(1.5y) = (6/5)*y.
Therefore, the price relative for 1977 is:
- Price relative for 1977 = y/x * 100
To find the reduce date, we need to find the year in which the price relative is less than 100 (i.e. when the price of the commodity decreased compared to the base year 1975).
Let the reduce date be z.
Then, the price of the commodity in year z is (4/5)*(1.5y) = (6/5)*y.
Therefore, the price relative for year z is:
- Price relative for year z = (6/5)*y/x * 100
Since the price relative for year z is less than 100, we have:
(6/5)*y/x * 100 < />
=> (6/5)*y/x < />
=> y/x < />
Substituting the value of y/x from the price relatives for 1975 and 1977, we get:
(6/5)*y/x = (6/5)*(y/x) * (66.67/100) * (100/y)
=> (6/5)*(y/x) * (2/3) < />
=> (y/x) < />
Therefore, the reduce date is the year in which the price of the commodity was less than 83.33% of the price in 1974.
From the given options, the only year that satisfies this condition is option B: 150,80.
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In 1976 the average price of a commodity was 20% more than that in 1975 but 20% less than that in 1974 and more over it was 50% more than that in 1977. The price relatives using 1975 as base year (1975 price relative = 100) then the reduce date is :a)8,.75b)150,80c)75,125d)None of these.Correct answer is option 'B'. Can you explain this answer?
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