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If the price of an article is increased by 15%, then by how much the household should decrease their consumption so as to keep his expenditure same.
- a)13(1/23)%
- b)13(2/23)%
- c)11(1/23)%
- d)11(2/23)%
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
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If the price of an article is increased by 15%, then by how much the h...
Answer – 1.13(1/23)% Explanation : Decrease in expenditure = (15/115)*100 = 300/23 %
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If the price of an article is increased by 15%, then by how much the h...
Problem:
The price of an article is increased by 15%. How much should the household decrease their consumption to keep their expenditure the same?
Solution:
To solve this problem, we need to understand the relationship between price, consumption, and expenditure.
Let's assume the initial price of the article is P and the initial consumption is C. Therefore, the initial expenditure (E1) can be calculated as:
E1 = P * C
After the price increase of 15%, the new price (P') can be calculated as:
P' = P + (15% of P)
= P + (0.15 * P)
= P * 1.15
To keep the expenditure the same, the household should decrease their consumption by a certain percentage. Let's assume this percentage as x. Therefore, the new consumption (C') can be calculated as:
C' = C - (x% of C)
= C - (0.01 * x * C)
= C * (1 - 0.01 * x)
The new expenditure (E2) can be calculated as:
E2 = P' * C'
= (P * 1.15) * (C * (1 - 0.01 * x))
= P * C * (1.15) * (1 - 0.01 * x)
Since we want to keep the expenditure the same, E1 and E2 should be equal:
E1 = E2
P * C = P * C * (1.15) * (1 - 0.01 * x)
Simplifying the equation:
1 = 1.15 * (1 - 0.01 * x)
1/1.15 = 1 - 0.01 * x
0.8696 = 1 - 0.01 * x
0.01 * x = 1 - 0.8696
0.01 * x = 0.1304
x = 0.1304 / 0.01
x = 13.04
Therefore, the household should decrease their consumption by approximately 13.04% to keep their expenditure the same.
Answer:
The correct option is a) 13(1/23)%.
The price of an article is increased by 15%. How much should the household decrease their consumption to keep their expenditure the same?
Solution:
To solve this problem, we need to understand the relationship between price, consumption, and expenditure.
Let's assume the initial price of the article is P and the initial consumption is C. Therefore, the initial expenditure (E1) can be calculated as:
E1 = P * C
After the price increase of 15%, the new price (P') can be calculated as:
P' = P + (15% of P)
= P + (0.15 * P)
= P * 1.15
To keep the expenditure the same, the household should decrease their consumption by a certain percentage. Let's assume this percentage as x. Therefore, the new consumption (C') can be calculated as:
C' = C - (x% of C)
= C - (0.01 * x * C)
= C * (1 - 0.01 * x)
The new expenditure (E2) can be calculated as:
E2 = P' * C'
= (P * 1.15) * (C * (1 - 0.01 * x))
= P * C * (1.15) * (1 - 0.01 * x)
Since we want to keep the expenditure the same, E1 and E2 should be equal:
E1 = E2
P * C = P * C * (1.15) * (1 - 0.01 * x)
Simplifying the equation:
1 = 1.15 * (1 - 0.01 * x)
1/1.15 = 1 - 0.01 * x
0.8696 = 1 - 0.01 * x
0.01 * x = 1 - 0.8696
0.01 * x = 0.1304
x = 0.1304 / 0.01
x = 13.04
Therefore, the household should decrease their consumption by approximately 13.04% to keep their expenditure the same.
Answer:
The correct option is a) 13(1/23)%.
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