Which of the following is/are true ? (A) If the selling price (SP) of an…
2024
Which of the following is/are true ?
(A) If the selling price (SP) of an article is ₹ 40 and the gain is 15 %, the cost price (CP) of the article is ₹ 32
(B) A man bought a toy for ₹ 150 and sold it at a profit of 8 %. He sold the toy for ₹ 162
(C) A man buys a cycle for ₹ 500, but due to some problem, he sells it for ₹ 400. He thus incurs a loss of 22 %
(D) Cost price of an article, if its SP is ₹ 210 and the loss is 30 %, is ₹ 300.
Choose the correct answer from the options given below :
Answer: C. (B) and (D) Only — Concept: in every profit-and-loss calculation the gain or loss percentage is reckoned on the COST PRICE, never on the selling price. That single rule fixes…
- A.
(A) Only
- B.
(A) and (D) Only
- C.
(B) and (D) Only
- D.
(B) and (C) Only
Show answer & explanation
Correct answer: C
Concept: in every profit-and-loss calculation the gain or loss percentage is reckoned on the COST PRICE, never on the selling price. That single rule fixes all four working forms: SP = CP × (1 + gain% ÷ 100) and SP = CP × (1 − loss% ÷ 100), and, inverted, CP = SP ÷ (1 + gain% ÷ 100) and CP = SP ÷ (1 − loss% ÷ 100). Equivalently, loss% = (CP − SP) ÷ CP × 100.
Application — test each claim against its own figures:
SP ₹ 40 with a 15 % gain. Using CP = SP ÷ (1 + gain% ÷ 100): CP = 40 ÷ 1.15 = ₹ 34.78 (to 2 decimal places). The figure ₹ 32 stated in this claim would instead give SP = 32 × 1.15 = ₹ 36.80, so the claim does not hold.
CP ₹ 150 with an 8 % profit. Using SP = CP × (1 + gain% ÷ 100): SP = 150 × 1.08 = ₹ 162, which is exactly the figure stated in this claim, so the claim holds.
CP ₹ 500 sold for ₹ 400. Loss = 500 − 400 = ₹ 100, so loss% = (100 ÷ 500) × 100 = 20 %. The claim states 22 %, so the claim does not hold.
SP ₹ 210 with a 30 % loss. Using CP = SP ÷ (1 − loss% ÷ 100): CP = 210 ÷ 0.70 = ₹ 300, which is exactly the figure stated in this claim, so the claim holds.
Cross-check — the two rejected claims are not rescued by the usual base error either: reckoning the percentage on the selling price gives 40 − 0.15 × 40 = ₹ 34 (still not ₹ 32) and 100 ÷ 400 × 100 = 25 % (still not 22 %). The full comparison:
Claim | Correct value | Value stated |
|---|---|---|
CP when SP = ₹ 40, gain 15 % | ₹ 34.78 | ₹ 32 |
SP when CP = ₹ 150, profit 8 % | ₹ 162 | ₹ 162 |
Loss % when CP = ₹ 500, SP = ₹ 400 | 20 % | 22 % |
CP when SP = ₹ 210, loss 30 % | ₹ 300 | ₹ 300 |
Only the toy statement (B) and the ₹ 210 selling-price statement (D) survive the check, so the set of true statements is (B) and (D) Only.