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The price of rice increases by 20% and hence the expenditure of a family increases by 10%. Find out by what percent the consumption has been decreased?
- a)8(1/3) %
- b)8(2/3) %
- c)8.5%
- d)9%
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The price of rice increases by 20% and hence the expenditure of a fam...
20% = 1/5
= 6/30 : 5/30(When expenditure remains same)
but new exp is 10% more
i.e expenditure = 33
Hence, new consumption = x
6 × x = 33
X = 5.5
New consumption = 5.5
= 8(1/3) %
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The price of rice increases by 20% and hence the expenditure of a fam...
Given:
- Price of rice increases by 20%.
- Expenditure of a family increases by 10%.
To Find:
- By what percent the consumption has been decreased.
Assumptions:
- Let the original price of rice be P and the original consumption of rice be C.
Calculations:
1. Initially, the expenditure on rice (E1) is given by:
E1 = P * C
2. After the price increase of 20%, the new price of rice (P2) is given by:
P2 = P + (20/100) * P
= P + 0.2P
= 1.2P
3. After the expenditure increase of 10%, the new expenditure on rice (E2) is given by:
E2 = E1 + (10/100) * E1
= E1 + 0.1E1
= E1 + 0.1 * (P * C)
= P * C + 0.1 * P * C
= P * C * (1 + 0.1)
= 1.1 * P * C
4. The new consumption of rice (C2) can be calculated by dividing the new expenditure by the new price:
C2 = E2 / P2
= (1.1 * P * C) / (1.2P)
= 1.1C / 1.2
5. The percentage decrease in consumption can be calculated as:
Decrease in consumption = (C - C2) / C * 100
Simplifying the expression:
Decrease in consumption = (C - 1.1C/1.2) / C * 100
= (C * (1 - 1.1/1.2)) / C * 100
= (C * (0.1/1.2)) / C * 100
= (0.1/1.2) * 100
= 0.083333 * 100
= 8.3333
Approximating to the nearest percent:
Decrease in consumption ≈ 8%
Conclusion:
The consumption of rice has been decreased by approximately 8%. Therefore, the correct answer is option 'A' (8(1/3) %).
- Price of rice increases by 20%.
- Expenditure of a family increases by 10%.
To Find:
- By what percent the consumption has been decreased.
Assumptions:
- Let the original price of rice be P and the original consumption of rice be C.
Calculations:
1. Initially, the expenditure on rice (E1) is given by:
E1 = P * C
2. After the price increase of 20%, the new price of rice (P2) is given by:
P2 = P + (20/100) * P
= P + 0.2P
= 1.2P
3. After the expenditure increase of 10%, the new expenditure on rice (E2) is given by:
E2 = E1 + (10/100) * E1
= E1 + 0.1E1
= E1 + 0.1 * (P * C)
= P * C + 0.1 * P * C
= P * C * (1 + 0.1)
= 1.1 * P * C
4. The new consumption of rice (C2) can be calculated by dividing the new expenditure by the new price:
C2 = E2 / P2
= (1.1 * P * C) / (1.2P)
= 1.1C / 1.2
5. The percentage decrease in consumption can be calculated as:
Decrease in consumption = (C - C2) / C * 100
Simplifying the expression:
Decrease in consumption = (C - 1.1C/1.2) / C * 100
= (C * (1 - 1.1/1.2)) / C * 100
= (C * (0.1/1.2)) / C * 100
= (0.1/1.2) * 100
= 0.083333 * 100
= 8.3333
Approximating to the nearest percent:
Decrease in consumption ≈ 8%
Conclusion:
The consumption of rice has been decreased by approximately 8%. Therefore, the correct answer is option 'A' (8(1/3) %).
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The price of rice increases by 20% and hence the expenditure of a family increases by 10%. Find out by what percent the consumption has been decreased?a)8(1/3) %b)8(2/3) %c)8.5%d)9%Correct answer is option 'A'. Can you explain this answer?
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