The price of oil increases by 25%. If the expenditure is not allowed to…
2011
The price of oil increases by 25%. If the expenditure is not allowed to increase, what is the ratio of the reduction in consumption to the original consumption?
Answer: C. 1 : 5 — ConceptWhen expenditure stays constant, price and consumption vary inversely. If price is multiplied by a factor k, consumption must be divided by k so that…
- A.
1 : 3
- B.
1 : 4
- C.
1 : 5
- D.
1 : 6
Attempted by 2 students.
Show answer & explanation
Correct answer: C
Concept
When expenditure stays constant, price and consumption vary inversely. If price is multiplied by a factor k, consumption must be divided by k so that price × consumption remains unchanged.
Application
Let the original price be P and the original consumption be C. The original expenditure is PC.
After a 25% increase, the new price is 1.25P = 5P/4. If the new consumption is Cnew, then (5P/4) × Cnew = PC.
Cancelling P gives (5/4) × Cnew = C, so Cnew = (4/5)C.
The reduction is C − (4/5)C = (1/5)C. Therefore, reduction : original consumption = (C/5) : C = 1 : 5.
Cross-check
Substitution gives (5P/4) × (4C/5) = PC, so the expenditure is unchanged. Hence the required ratio is 1 : 5.