If the price of gold increases by 30%, by how much must the quantity of…
2024
If the price of gold increases by 30%, by how much must the quantity of ornaments be reduced so that expenditure remains the same?
- A.
30%
- B.
23 + (1/13)%
- C.
27/13%
- D.
19%
Attempted by 9 students.
Show answer & explanation
Correct answer: B
Solution: compute the required reduction in quantity when price increases by 30%.
Let the original price be P and original quantity be Q.
New price = 1.3 × P. To keep expenditure the same: P · Q = 1.3P · Q_new.
Solve for Q_new: Q_new = Q / 1.3 = (10/13)Q.
Reduction = Q − Q_new = Q − (10/13)Q = (3/13)Q, so the fraction reduced is 3/13 ≈ 0.230769.
As a percentage: (3/13) × 100% = 300/13% = 23 + (1/13)% ≈ 23.077%.
Answer: Reduce the quantity by 23 + (1/13)% (approximately 23.08%).