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- Question
Consider the following statements: 1) The perimeter of a triangle is greater than the sum of its three medinas. 2) In any triangle ABC, if D is any point on BC, then AB + BC + CA > 2AD. Which of the above statements is/are correct?
Options- A. 1 only
- B. 2 only
- C. Both 1 and 2
- D. Neither 1 nor 2
- Correct Answer
- Both 1 and 2
ExplanationLet ABC be the triangle and D. E and F are midpoints of BC, CA and AB respectively.Recall that the sum of two sides of a triangle is greater than twice the median bisecting the third side,(Theorem to be remembered)Hence in ?ABD, AD is a median?AB + AC > 2(AD)Similarly, we getBC + AC > 2CFBC + AB > 2BEOn adding the above inequations, we get(AB + AC) + (BC + AC) + (BC + AB )> 2AD + 2CD + 2BE2(AB + BC + AC) > 2(AD + BE + CF)?AB + BC + AC > AD + BE +CF2.To prove: AB + BC + CA > 2ADConstruction: AD is joinedProof: In triangle ABD,AB + BD > AD [because, the sum of any two sides of a triangle is always greater than thethird side]----1In triangle ADC,AC + DC > AD [because, the sum of any twosides of a triangle is always greater than thethird side]----2Adding 1 and 2 we get,AB + BD + AC + DC > AD + AD=> AB + (BD + DC) + AC > 2AD=> AB + BC + AC > 2ADHence proved - 1. A person sold an article for ? 3600 and got a profit of 20%. Had he sold the article for ? 3150, how much profit would he have got?
Options- A. 4%
- B. 5%
- C. 6%
- D. 10% Discuss
- 2. Two lots of onions with equal quantity, one costing ? 10 per kg and the other costing ? 15 per kg, are mixed together and whole lot is sold at ? 15 per kg. What is the profit or loss?
Options- A. 10% loss
- B. 10% profit
- C. 20% profit
- D. 20% loss Discuss
- 3. By selling 32 orange for ? 30 a man loses 25%. How many oranges should be sold for ? 24 so as to gain 20% in the transaction?
Options- A. 16
- B. 24
- C. 32
- D. 28 Discuss
- 4. Kamlesh purchased 120 reams of paper at ? 100 per ream and the expenditure on transport was ? 480. He had to pay an octroi duty of 50 paise per ream and the coolie charges were ? 60. What should he charge per ream to gain 40%?
Options- A. ?155
- B. ? 147
- C. ? 138
- D. ? 165 Discuss
- 5. A dishonest dealer sells his goods at 10% loss on cost price and uses 30% less weight. What is his profit or loss per cent?
Options- A. 284/7 % loss
- B. 283/7 % gain
- C. 283/7 % loss
- D. 284/7 % gain Discuss
- 6. A man sold two houses for ? 96000 each. In the sale of the first house, he incurred 20% profit and in the sale of the second, he incurred 20% loss. what is the gain or loss percentage in total?
Options- A. 6% gain
- B. 6% loss
- C. 4% gain
- D. 4% loss Discuss
- 7. A man sold two watches, each for ? 495. If he gained 10% on one watch and suffered a loss of 10% on the other, then what is the loss of gain percentage in the transaction?
Options- A. 1 % gain
- B. 1% loss
- C. 100/99% loss
- D. Neither gain nor loss Discuss
- 8. A person sold an article for ? 136 and got 15% loss, had he sold it for ? N, he would have got a profit of 15%. Which one of the following is correct?
Options- A. 190 < N < 200
- B. 180 < N < 190
- C. 170 < N < 180
- D. 160 < N < 170 Discuss
- 9. A Seller uses 920g in place of one kg to sell his goods. When he sells his article at 15% gain on cost price, the actual percentage of profit is?
Options- A. 20%
- B. 15%
- C. 25%
- D. 30% Discuss
- 10. A shopkeeper sells transistors at 15% above its cost price. If he had bought it at 5% more than what he paid for it and sold it for ? 6 more, he would have gained 10%. The cost price of the transistor is?
Options- A. ? 800
- B. ? 1000
- C. ? 1200
- D. ? 1400 Discuss
More questions
Correct Answer: 5%
Explanation:
Let the cost price of the article be ? N.
Now, N + 20N/100 = 3600
? 120N/100 = 3600
? N = 3000
Now, profit percentage when the article is sold for ? 3150 = [(3150 - 3000)/3000] x 100
= (150/3000) x 100 = 5%
Correct Answer: 20% profit
Explanation:
Let each lot of onion-contain N kg onion,
Then total cost price of these two lots together = 10N + 15N = 25N
Selling price of whole lot = 15 x (N + N) = 15 x 2N = 30N
Profit percentage = [(30N - 25N)/25N] x 100 %
= (5/25) x 100%
= 20%
Correct Answer: 24
Explanation:
Let the cost price be ? N.
SP of 1 orange = ? 30/32 = ? 15/16
According to the question, 75N/100 = 15/16
? N = [(15 x 100)/75] x 16 = ? 5/4
SP of 1 orange with 20% profit = ? [(5/4) x 120]/100 = ? 3/2
? In ? 3/2, the number of oranges sold = 1
? in ? 24, the number of oranges sold = (2/3) x 24 = 16
Correct Answer: ? 147
Explanation:
Total cost price = ? (120 x 100) = ? 12000
Total expenditure = 480 + (1/2) x 120 + 60 = ? 600
Total cost price = 12000 + 600 = ? 126000
Gain = 40%
SP of 120 reams = 12600 x (140/100) = ? 17640
? SP per ream = 17640/120 = ? 147
Correct Answer: 284/7 % gain
Explanation:
Given that, a = 10% and b = 30%
According to the formula,
Required per cent = [(b - a)/(100 - b)] x 100
= [(30 - 10)/(100 - 30)] x 100
= (20/70) x 100 = 200/7%
= 284/7% profit
Correct Answer: 4% loss
Explanation:
Here, a = 20%
? Total loss percentage = a2/100 %
= (20 x 20)/100
= 4%
Correct Answer: 1% loss
Explanation:
Loss % = (a/10)2%
= (10/10)2%
= 1%
Correct Answer: 180 < N < 190
Explanation:
Cost price = (selling price x 100)/(100 - loss%)
= (136 x 100)/(100 - 15)
= (136 x 100)/85
= ? 160
Selling price (N) = 160 x (100 + 15)/100 = (160 x 115)/100
= ? 184
? Option (b) is correct because
[180 < N < 190].
Correct Answer: 25%
Explanation:
Let cost price = ? 1000
? Actual cost price = ? 920
Selling price = (1000 x 115)/100 = ?1150
? Actual profit percentage = (1150 - 920)/(920 x 100) = 25%
Correct Answer: ? 1200
Explanation:
Let cost price of transistor = ? N
According to the question,
CP of transistor = (N x 105)/100
And SP of transistor = (115 x N)/100 + 6
? Profit percentage = (SP - CP)/CP x 100
? 10 = [[(115N/100) + 6 - (105N/100)] / (105N/100)] x 100
? 10 = [(10N + 600) x 100]/ 105N
? 105N = 100N + 6000
? 5N = 6000
? N= ? 1200
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