This lesson explains the terms, gives each formula with its reason, and solves three examples. It also lists the traps that cost marks.
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Q1. An article is bought for Rs. 257 and sold at a loss of 9%. What is the selling price?
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Answer: B
Let CP = Rs. 257, with a loss of 9%. SP = CP x (100 – 9)/100 = 257 x 91/100. 257 x 91 = 23387, so SP = 23387/100 = 233.87. So SP = Rs. 233.87. Check: |SP – CP|/CP x 100 = |233.87 – 257|/257 x 100 = 9%, matching the given 9% loss.
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Q2. An article is bought for Rs. 1095 and sold at a gain of 76%. What is the selling price?
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Answer: A
Let CP = Rs. 1095, with a gain of 76%. SP = CP x (100 + 76)/100 = 1095 x 176/100. 1095 x 176 = 192720, so SP = 192720/100 = 1927.2. So SP = Rs. 1927.2. Check: |SP – CP|/CP x 100 = |1927.2 – 1095|/1095 x 100 = 76%, matching the given 76% gain.
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Q3. An article is bought for Rs. 1230 and sold at a loss of 23%. What is the selling price?
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Answer: D
Let CP = Rs. 1230, with a loss of 23%. SP = CP x (100 – 23)/100 = 1230 x 77/100. 1230 x 77 = 94710, so SP = 94710/100 = 947.1. So SP = Rs. 947.1. Check: |SP – CP|/CP x 100 = |947.1 – 1230|/1230 x 100 = 23%, matching the given 23% loss.
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Q4. An article is bought for Rs. 138 and sold for Rs. 69. What is the loss percent?
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Answer: C
Let CP = Rs. 138 and SP = Rs. 69. The loss amount is |SP – CP| = |69 – 138| = 69, so the loss is Rs. 69. Loss% = (loss amount / CP) x 100 = 69/138 x 100 = 50%. Check: CP x (100 – 50)/100 = 138 x 50/100 = 69, which matches SP = Rs. 69.
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Q5. An article is bought for Rs. 256 and sold for Rs. 320. What is the gain percent?
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Answer: A
Let CP = Rs. 256 and SP = Rs. 320. The gain amount is |SP – CP| = |320 – 256| = 64, so the gain is Rs. 64. Gain% = (gain amount / CP) x 100 = 64/256 x 100 = 25%. Check: CP x (100 + 25)/100 = 256 x 125/100 = 320, which matches SP = Rs. 320.
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Q6. An article is bought for Rs. 315 and sold for Rs. 252. What is the loss percent?
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Answer: D
Let CP = Rs. 315 and SP = Rs. 252. The loss amount is |SP – CP| = |252 – 315| = 63, so the loss is Rs. 63. Loss% = (loss amount / CP) x 100 = 63/315 x 100 = 20%. Check: CP x (100 – 20)/100 = 315 x 80/100 = 252, which matches SP = Rs. 252.
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Q7. An article is bought for Rs. 534 and sold for Rs. 267. What is the loss percent?
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Answer: B
Let CP = Rs. 534 and SP = Rs. 267. The loss amount is |SP – CP| = |267 – 534| = 267, so the loss is Rs. 267. Loss% = (loss amount / CP) x 100 = 267/534 x 100 = 50%. Check: CP x (100 – 50)/100 = 534 x 50/100 = 267, which matches SP = Rs. 267.
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Q8. An article is bought for Rs. 1560 and sold for Rs. 2496. What is the gain percent?
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Answer: B
Let CP = Rs. 1560 and SP = Rs. 2496. The gain amount is |SP – CP| = |2496 – 1560| = 936, so the gain is Rs. 936. Gain% = (gain amount / CP) x 100 = 936/1560 x 100 = 60%. Check: CP x (100 + 60)/100 = 1560 x 160/100 = 2496, which matches SP = Rs. 2496.
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Q9. An article is bought for Rs. 150 and sold for Rs. 192. What is the gain percent?
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Answer: A
Let CP = Rs. 150 and SP = Rs. 192. The gain amount is |SP – CP| = |192 – 150| = 42, so the gain is Rs. 42. Gain% = (gain amount / CP) x 100 = 42/150 x 100 = 28%. Check: CP x (100 + 28)/100 = 150 x 128/100 = 192, which matches SP = Rs. 192.
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Q10. An article is bought for Rs. 65 and sold for Rs. 78. What is the gain percent?
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Answer: D
Let CP = Rs. 65 and SP = Rs. 78. The gain amount is |SP – CP| = |78 – 65| = 13, so the gain is Rs. 13. Gain% = (gain amount / CP) x 100 = 13/65 x 100 = 20%. Check: CP x (100 + 20)/100 = 65 x 120/100 = 78, which matches SP = Rs. 78.
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Q11. An article is bought for Rs. 350 and sold for Rs. 196. What is the loss percent?
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Answer: C
Let CP = Rs. 350 and SP = Rs. 196. The loss amount is |SP – CP| = |196 – 350| = 154, so the loss is Rs. 154. Loss% = (loss amount / CP) x 100 = 154/350 x 100 = 44%. Check: CP x (100 – 44)/100 = 350 x 56/100 = 196, which matches SP = Rs. 196.
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Q12. An article is bought for Rs. 1850 and sold for Rs. 1517. What is the loss percent?
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Answer: B
Let CP = Rs. 1850 and SP = Rs. 1517. The loss amount is |SP – CP| = |1517 – 1850| = 333, so the loss is Rs. 333. Loss% = (loss amount / CP) x 100 = 333/1850 x 100 = 18%. Check: CP x (100 – 18)/100 = 1850 x 82/100 = 1517, which matches SP = Rs. 1517.
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Q13. An article is bought for Rs. 1100 and sold for Rs. 1254. What is the gain percent?
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Answer: A
Let CP = Rs. 1100 and SP = Rs. 1254. The gain amount is |SP – CP| = |1254 – 1100| = 154, so the gain is Rs. 154. Gain% = (gain amount / CP) x 100 = 154/1100 x 100 = 14%. Check: CP x (100 + 14)/100 = 1100 x 114/100 = 1254, which matches SP = Rs. 1254.
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Q14. An article is bought for Rs. 425 and sold for Rs. 289. What is the loss percent?
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Answer: D
Let CP = Rs. 425 and SP = Rs. 289. The loss amount is |SP – CP| = |289 – 425| = 136, so the loss is Rs. 136. Loss% = (loss amount / CP) x 100 = 136/425 x 100 = 32%. Check: CP x (100 – 32)/100 = 425 x 68/100 = 289, which matches SP = Rs. 289.
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Q15. An article is bought for Rs. 1408 and sold for Rs. 1760. What is the gain percent?
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Answer: C
Let CP = Rs. 1408 and SP = Rs. 1760. The gain amount is |SP – CP| = |1760 – 1408| = 352, so the gain is Rs. 352. Gain% = (gain amount / CP) x 100 = 352/1408 x 100 = 25%. Check: CP x (100 + 25)/100 = 1408 x 125/100 = 1760, which matches SP = Rs. 1760.
Related topics: Profit and Loss: Formulas, Shortcuts and Solved Examples
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