If you double the cost price of a product and the selling price remains constant the profit...
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If you double the cost price of a product and the selling price remains constant the profit of the product is reduced to one third. Find the profit/loss % if the cost price of the product will be thrice.
Show answer & explanation
Original profit is (SP - CP). When cost doubles to 2·CP with SP constant, profit becomes (SP - 2·CP) = (1/3)(SP - CP). Solving yields SP = 5·CP/2. When cost triples to 3·CP, the new profit is 5·CP/2 - 3·CP = -CP/2, a loss of 50%. However, recalculating loss percentage on the new cost: loss% = (CP/2)/(3·CP) × 100 = 16.67% loss.
Step-by-step Derivation:
Let original CP = C, SP = S, and profit P = S - C.
Condition 1: When cost doubles, profit becomes one-third.
New profit = S - 2C = (1/3)(S - C)
⟹ 3(S - 2C) = S - C
⟹ 3S - 6C = S - C
⟹ 2S = 5C
⟹ S = 2.5C
Original profit = 2.5C - C = 1.5C (or 150% profit initially)
Condition 2: When cost triples to 3C, with SP = 2.5C:
New result = 2.5C - 3C = -0.5C (a loss)
Loss% = (Loss / New CP) × 100
= (0.5C / 3C) × 100
= (1/6) × 100
= 16.67%