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- Question
Two equal circles intersect such that each passes through the centre of the other. If the length of the common chord of the circles is 10?3 cm, then what is the diameter of the circle?
Options- A. 10 cm
- B. 15 cm
- C. 20 cm
- D. 30 cm
- Correct Answer
- 20 cm
ExplanationLet there be 2 circles with centre O1 and OAB is the common chord
Since both passes through the center of each other as shown in figure
So O1O is the radius of both
Let O1O = r = AO1= AO
AX = AB / 2 = 5?3 cm (since OX perpendicular to chord bisects it)
AOO1 forms an equilateral triangle with on side = radius = r
Sin 60 = ?3/2 = AX / AO = 5?3/r
So r = 10 cm
So diameter = 20 cm
- 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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