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deepshikhasingh15
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Time ended
G8 Comparing quantities
Math quiz helps us to enhance brains neural network.
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1) If the compound interest on a sum for 2 years at 12% p.a. is ₹2544, find the principal.
A = P(1.12)^2 = P × 1.2544 CI = A − P = 1.2544P − P = 0.2544P = 2544 ⇒ P = 2544 / 0.2544 = ₹10,000
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2) A man sold a watch at a loss of 4%. If he had sold it for ₹20 more, he would have gained 4%. Find the cost price of the watch.
Let the CP be x. Loss case: SP = x − 0.04x = 0.96x Gain case: SP = x + 0.04x = 1.04x Difference = 1.04x − 0.96x = 0.08x = ₹20 ⇒ x = ₹250
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3) A man sells an article at a loss of 10%. If he had sold it for ₹30 more, he would have gained 5%. Find the cost price
Let CP = x Then: x − 10% of x + 30 = x + 5% of x ⇒ 0.9x + 30 = 1.05x ⇒ 30 = 0.15x ⇒ x = ₹200
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4) At what rate percent will ₹5,000 amount to ₹6,000 in 4 years?
SI = 1000 Rate = (SI × 100) / (P × T) = (1000 × 100) / (5000 × 4) = 5%
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5) By selling a pen for ₹54, a man gains 8%. What is the cost price of the pen?
SP = 108% of CP ⇒ CP = 54 / 1.08 = ₹50
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6) If the compound interest on ₹10,000 in 2 years is ₹2,100, find the rate of interest (compounded annually).
CI = P[(1 + r/100)^2 − 1] = 2100 (1 + r/100)^2 = 1.21 ⇒ r = 10%
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7) Find the single equivalent discount for successive discounts of 25% and 20%.
Net discount = a + b − (ab/100) = 25 + 20 − 5 = 40%
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8) A shopkeeper allows 20% discount and still gains 25%. Find the marked price if cost price is ₹600.
Let MP = x, SP = x × 0.80 Profit = 25% ⇒ SP = 600 × 1.25 = ₹750 0.8x = 750 ⇒ x = ₹937.50 (No exact match; closest correct MP = ₹937.50)
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9) A shirt’s price is increased by 15%. If the original price was $80, what is the new price?
Increase = 15% of $80 = 0.15 × $80 = $12. New price = $80 + $12 = $92.
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10) A shopkeeper gains 10% on selling an article for ₹550. What is the cost price of the article?
SP = 550, Gain = 10% CP = SP / 1.10 = 550 / 1.10 = ₹500
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11) A quantity increases by 20% and then by another 30%. What is the total percentage increase in the quantity?
Total % increase = a + b + (ab/100) = 20 + 30 + (20×30)/100 = 50 + 6 = 56%
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12) A product is marked at ₹500. Two successive discounts of 10% and 5% are given. What is the final price
First discount: 10% of 500 = 50 ⇒ New price = 450 Second discount: 5% of 450 = 22.50 ⇒ Final price = ₹427.50
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13) A trader allows a 15% discount on the marked price and still makes a profit of 20%. If the marked price is ₹1000, what is the cost price?
SP = MP − Discount = 1000 − 150 = ₹850 Let CP be x. 850 = x + 20% of x = 1.2x ⇒ x = 850 / 1.2 = ₹708.33 (approx), closest is ₹700
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14) How much time will ₹7,500 take to earn ₹1,125 at 6% p.a.?
= (SI × 100) / (P × R) = (1125 × 100) / (7500 × 6) = 2.5 years
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15) The price of a commodity increases by 25% and then decreases by 20%. What is the net percentage change in price?
Let initial price be 100 After 25% increase ⇒ 125 After 20% decrease ⇒ 125 × 0.8 = 100 New price = 100 ⇒ No change But wait—let’s double-check Initial = 100 Increase of 25% = 125 Decrease of 20% on 125 = 125 − 25 = 100 So net change = 0% ⇒ Correct answer: A. 0%
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16) If ₹4,000 becomes ₹4,840 in 2 years at compound interest compounded annually, what is the rate of interest?
A = P(1 + r/100)^2 ⇒ 4840 = 4000(1 + r/100)^2 (1 + r/100)^2 = 1.21 ⇒ r = 10%
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17) A shopkeeper marks an article at ₹800 and allows a discount of 20%. He still makes a profit of 25%. What is the cost price of the article?
Selling Price = 800 − 20% of 800 = 800 − 160 = ₹640 Let cost price be x. Profit = 25% ⇒ SP = 1.25x 640 = 1.25x ⇒ x = 640 / 1.25 = ₹512
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18) A person sells two items at ₹1,200 each. On one he gains 20% and on the other he loses 20%. Find the net result
If same SP and equal gain/loss %, net result is always a loss = (common%)²/100 ⇒ (20²)/100 = 400/100 = 4% loss
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19) The ratio of the number of red balls to blue balls in a bag is 2:3. If there are 10 red balls, how many blue balls are there?
Let’s use the ratio to set up an equation. Red:Blue = 2:3. If red = 10, then blue = (3/2) × 10 = 15.
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20) An article is sold at 20% profit and then bought again and sold at 20% loss. What is the overall profit or loss percent?
Net change = x − y − (xy/100) = 20 − 20 − 4 = −4% ⇒ 4% loss
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