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Artithmetic - Percentages (Profit/Loss, Interest, Markups)

Arithmetic GMAT GRE Mathematics Practice Set
100 MCQs
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1
A value increases from 226 to 339. What is the percentage increase?
Medium
ExplanationPercentage increase = ((339 − 226) / 226) × 100 = 50%.
2
A shop offers successive discounts of 15% and 16% on an item marked at Rs. 6000. What is the final selling price?
Medium
ExplanationFinal price = 6000 × (1 − 15/100) × (1 − 16/100) = Rs. 4284.
3
A sum of Rs. 6015 at 20% simple interest per annum earns Rs. 1203 in interest. For how many years was it invested?
Medium
ExplanationTime = (SI × 100) / (P × R) = (1203 × 100) / (6015 × 20) = 1 year.
4
An interest rate rises from 5% to 31%. By how many percentage points did it increase?
Medium
ExplanationA percentage-point increase is a simple subtraction: 31% − 5% = 26 percentage points.
5
What single discount is equivalent to two successive discounts of 2% and 48%?
Medium
ExplanationEquivalent discount = 100 − (100−2)(100−48)/100 = 49.04%.
6
What is the simple interest on Rs. 12182 at 6% per annum for 4 years?
Medium
ExplanationSimple Interest = (P × R × T) / 100 = (12182 × 6 × 4) / 100 = Rs. 2923.68.
7
A shopkeeper buys an item for Rs. 295 and sells it for Rs. 236. What is the loss percentage?
Medium
ExplanationLoss % = ((CP − SP) / CP) × 100 = ((295 − 236) / 295) × 100 = 20%.
8
What is 20% of 45% of 432?
Medium
Explanation20% of 45% of 432 = (20/100) × (45/100) × 432 = 38.88.
9
What is 15% of 366?
Medium
Explanation15% of 366 = (15/100) × 366 = 54.9.
10
What is the difference between the compound interest and simple interest on Rs. 3125 at 8% per annum for 2 years?
Medium
ExplanationFor 2 years, the difference between CI and SI is always P × (R/100)^2 = 3125 × (8/100)^2 = Rs. 20.
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11
An interest rate rises from 40% to 60%. By how many percentage points did it increase?
Medium
ExplanationA percentage-point increase is a simple subtraction: 60% − 40% = 20 percentage points.
12
What single discount is equivalent to two successive discounts of 25% and 6%?
Medium
ExplanationEquivalent discount = 100 − (100−25)(100−6)/100 = 29.5%.
13
An item is priced at Rs. 1360 before tax. With a sales tax of 12.5%, what is the total price?
Medium
ExplanationTotal price = Price × (1 + 12.5/100) = 1360 × 1.1250 = Rs. 1530.
14
A value is first increased by 40% and then decreased by 25%. What is the overall net percentage change?
Medium
ExplanationStarting with 100: after the first change it becomes 140.00, and after the second change it becomes 105.00 — a net change of +5% from the original 100.
15
Rs. 4691 is invested at 13% simple interest per annum for 3 years. What is the total amount after 3 years?
Medium
ExplanationAmount = Principal + Interest = 4691 + 1829.49 = Rs. 6520.49.
16
By selling an item for Rs. 837, a trader incurs a loss of 55%. What was the cost price?
Medium
ExplanationCost price = SP / (1 − 55/100) = 837 / 0.4500 = Rs. 1860.
17
A value is first increased by 55% and then decreased by 4%. What is the overall net percentage change?
Medium
ExplanationStarting with 100: after the first change it becomes 155.00, and after the second change it becomes 148.80 — a net change of +48.8% from the original 100.
18
What is 45% of 25% of 1908?
Medium
Explanation45% of 25% of 1908 = (45/100) × (25/100) × 1908 = 214.65.
19
A value is first increased by 24% and then decreased by 90%. What is the overall net percentage change?
Medium
ExplanationStarting with 100: after the first change it becomes 124.00, and after the second change it becomes 12.40 — a net change of -87.6% from the original 100.
20
A shopkeeper marks up an item costing Rs. 677 by 2%. What is the markup amount (in Rs.)?
Medium
ExplanationMarkup amount = CP × 2/100 = 677 × 0.0200 = Rs. 13.54.
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21
Rs. 11629 is invested at 16% simple interest per annum for 1 year. What is the total amount after 1 year?
Medium
ExplanationAmount = Principal + Interest = 11629 + 1860.64 = Rs. 13489.64.
22
What is 24% of 30?
Medium
Explanation24% of 30 = (24/100) × 30 = 7.2.
23
An interest rate rises from 51% to 59%. By how many percentage points did it increase?
Medium
ExplanationA percentage-point increase is a simple subtraction: 59% − 51% = 8 percentage points.
24
Rs. 9305 is invested at 7.5% simple interest per annum for 2 years. What is the total amount after 2 years?
Medium
ExplanationAmount = Principal + Interest = 9305 + 1395.75 = Rs. 10700.75.
25
What is 32% of 138?
Medium
Explanation32% of 138 = (32/100) × 138 = 44.16.
26
An interest rate rises from 14% to 37%. By how many percentage points did it increase?
Medium
ExplanationA percentage-point increase is a simple subtraction: 37% − 14% = 23 percentage points.
27
A shopkeeper marks up an item costing Rs. 512 by 40%. What is the markup amount (in Rs.)?
Medium
ExplanationMarkup amount = CP × 40/100 = 512 × 0.4000 = Rs. 204.8.
28
What is the simple interest on Rs. 16218 at 10% per annum for 8 years?
Medium
ExplanationSimple Interest = (P × R × T) / 100 = (16218 × 10 × 8) / 100 = Rs. 12974.4.
29
A shop offers successive discounts of 36% and 15% on an item marked at Rs. 4750. What is the final selling price?
Medium
ExplanationFinal price = 4750 × (1 − 36/100) × (1 − 15/100) = Rs. 2584.
30
A sum of Rs. 5855 at 16% simple interest per annum earns Rs. 4684 in interest. For how many years was it invested?
Medium
ExplanationTime = (SI × 100) / (P × R) = (4684 × 100) / (5855 × 16) = 5 years.
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31
A shop offers successive discounts of 25% and 45% on an item marked at Rs. 3040. What is the final selling price?
Medium
ExplanationFinal price = 3040 × (1 − 25/100) × (1 − 45/100) = Rs. 1254.
32
A shopkeeper buys an item for Rs. 170 and sells it for Rs. 221. What is the profit percentage?
Medium
ExplanationProfit % = ((SP − CP) / CP) × 100 = ((221 − 170) / 170) × 100 = 30%.
33
An interest rate rises from 6% to 21%. What is the percent increase relative to the original rate?
Medium
ExplanationRelative percent increase = (((21 − 6) / 6) × 100 = 250%. (Note this differs from the 15-percentage-point change.)
34
A shopkeeper marks up an item costing Rs. 1180 by 32%. What is the markup amount (in Rs.)?
Medium
ExplanationMarkup amount = CP × 32/100 = 1180 × 0.3200 = Rs. 377.6.
35
What is the compound interest on Rs. 128 at 25% per annum, compounded annually, for 2 years?
Medium
ExplanationAmount = P(1 + R/100)^2 = 128 × (1 + 25/100)^2 = Rs. 200, so CI = Rs. 200 − Rs. 128 = Rs. 72.
36
What single discount is equivalent to two successive discounts of 35% and 40%?
Medium
ExplanationEquivalent discount = 100 − (100−35)(100−40)/100 = 61%.
37
An interest rate rises from 13% to 38%. By how many percentage points did it increase?
Medium
ExplanationA percentage-point increase is a simple subtraction: 38% − 13% = 25 percentage points.
38
An interest rate rises from 38% to 42%. By how many percentage points did it increase?
Medium
ExplanationA percentage-point increase is a simple subtraction: 42% − 38% = 4 percentage points.
39
Rs. 9088 is invested at 5% simple interest per annum for 3 years. What is the total amount after 3 years?
Medium
ExplanationAmount = Principal + Interest = 9088 + 1363.2 = Rs. 10451.2.
40
What is the simple interest on Rs. 2036 at 8% per annum for 5 years?
Medium
ExplanationSimple Interest = (P × R × T) / 100 = (2036 × 8 × 5) / 100 = Rs. 814.4.
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41
What single discount is equivalent to two successive discounts of 55% and 48%?
Medium
ExplanationEquivalent discount = 100 − (100−55)(100−48)/100 = 76.6%.
42
A sum of Rs. 5340 earns Rs. 1869 in simple interest over 5 years. What is the annual interest rate?
Medium
ExplanationRate = (SI × 100) / (P × T) = (1869 × 100) / (5340 × 5) = 7%.
43
An item marked at Rs. 2954 is sold at a discount of 50%. What is the selling price?
Medium
ExplanationSelling price = Marked price × (1 − 50/100) = 2954 × 0.5000 = Rs. 1477.
44
What is 24% of 550?
Medium
Explanation24% of 550 = (24/100) × 550 = 132.
45
What single discount is equivalent to two successive discounts of 50% and 5%?
Medium
ExplanationEquivalent discount = 100 − (100−50)(100−5)/100 = 52.5%.
46
What is the simple interest on Rs. 14973 at 5% per annum for 7 years?
Medium
ExplanationSimple Interest = (P × R × T) / 100 = (14973 × 5 × 7) / 100 = Rs. 5240.55.
47
A shopkeeper marks up an item costing Rs. 1727 by 30%. What is the markup amount (in Rs.)?
Medium
ExplanationMarkup amount = CP × 30/100 = 1727 × 0.3000 = Rs. 518.1.
48
At 20% simple interest per annum, a sum earns Rs. 5191 in 5 years. What is the principal?
Medium
ExplanationPrincipal = (SI × 100) / (R × T) = (5191 × 100) / (20 × 5) = Rs. 5191.
49
What is 85% of 489?
Medium
Explanation85% of 489 = (85/100) × 489 = 415.65.
50
Rs. 17323 is invested at 8% simple interest per annum for 4 years. What is the total amount after 4 years?
Medium
ExplanationAmount = Principal + Interest = 17323 + 5543.36 = Rs. 22866.36.
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51
By selling an item for Rs. 498, a trader incurs a loss of 25%. What was the cost price?
Medium
ExplanationCost price = SP / (1 − 25/100) = 498 / 0.7500 = Rs. 664.
52
What is the simple interest on Rs. 9220 at 4% per annum for 3 years?
Medium
ExplanationSimple Interest = (P × R × T) / 100 = (9220 × 4 × 3) / 100 = Rs. 1106.4.
53
A value is first decreased by 45% and then increased by 22%. What is the overall net percentage change?
Medium
ExplanationStarting with 100: after the first change it becomes 55.00, and after the second change it becomes 67.10 — a net change of -32.9% from the original 100.
54
What single discount is equivalent to two successive discounts of 12% and 8%?
Medium
ExplanationEquivalent discount = 100 − (100−12)(100−8)/100 = 19.04%.
55
An interest rate rises from 14% to 22%. By how many percentage points did it increase?
Medium
ExplanationA percentage-point increase is a simple subtraction: 22% − 14% = 8 percentage points.
56
What is the compound interest on Rs. 8125 at 12% per annum, compounded annually, for 2 years?
Medium
ExplanationAmount = P(1 + R/100)^2 = 8125 × (1 + 12/100)^2 = Rs. 10192, so CI = Rs. 10192 − Rs. 8125 = Rs. 2067.
57
Rs. 1173 is invested at 13% simple interest per annum for 7 years. What is the total amount after 7 years?
Medium
ExplanationAmount = Principal + Interest = 1173 + 1067.43 = Rs. 2240.43.
58
What is 20% of 5% of 204?
Medium
Explanation20% of 5% of 204 = (20/100) × (5/100) × 204 = 2.04.
59
What is the difference between the compound interest and simple interest on Rs. 1200 at 10% per annum for 2 years?
Medium
ExplanationFor 2 years, the difference between CI and SI is always P × (R/100)^2 = 1200 × (10/100)^2 = Rs. 12.
60
What is the simple interest on Rs. 658 at 3% per annum for 8 years?
Medium
ExplanationSimple Interest = (P × R × T) / 100 = (658 × 3 × 8) / 100 = Rs. 157.92.
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61
What is the simple interest on Rs. 3497 at 11% per annum for 7 years?
Medium
ExplanationSimple Interest = (P × R × T) / 100 = (3497 × 11 × 7) / 100 = Rs. 2692.69.
62
A sum of Rs. 14615 earns Rs. 23384 in simple interest over 8 years. What is the annual interest rate?
Medium
ExplanationRate = (SI × 100) / (P × T) = (23384 × 100) / (14615 × 8) = 20%.
63
A shop offers successive discounts of 12.5% and 12% on an item marked at Rs. 1100. What is the final selling price?
Medium
ExplanationFinal price = 1100 × (1 − 12.5/100) × (1 − 12/100) = Rs. 847.
64
Rs. 2040 is invested at 14% simple interest per annum for 1 year. What is the total amount after 1 year?
Medium
ExplanationAmount = Principal + Interest = 2040 + 285.6 = Rs. 2325.6.
65
By selling an item for Rs. 738, a trader incurs a loss of 18%. What was the cost price?
Medium
ExplanationCost price = SP / (1 − 18/100) = 738 / 0.8200 = Rs. 900.
66
What is the compound interest on Rs. 3125 at 8% per annum, compounded annually, for 2 years?
Medium
ExplanationAmount = P(1 + R/100)^2 = 3125 × (1 + 8/100)^2 = Rs. 3645, so CI = Rs. 3645 − Rs. 3125 = Rs. 520.
67
An interest rate rises from 49% to 68%. By how many percentage points did it increase?
Medium
ExplanationA percentage-point increase is a simple subtraction: 68% − 49% = 19 percentage points.
68
An interest rate rises from 50% to 76%. By how many percentage points did it increase?
Medium
ExplanationA percentage-point increase is a simple subtraction: 76% − 50% = 26 percentage points.
69
What is 6% of 166?
Medium
Explanation6% of 166 = (6/100) × 166 = 9.96.
70
A value is first increased by 95% and then decreased by 10%. What is the overall net percentage change?
Medium
ExplanationStarting with 100: after the first change it becomes 195.00, and after the second change it becomes 175.50 — a net change of +75.5% from the original 100.
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71
A shopkeeper marks up an item costing Rs. 70 by 25%. What is the markup amount (in Rs.)?
Medium
ExplanationMarkup amount = CP × 25/100 = 70 × 0.2500 = Rs. 17.5.
72
What is the difference between the compound interest and simple interest on Rs. 1200 at 10% per annum for 2 years?
Medium
ExplanationFor 2 years, the difference between CI and SI is always P × (R/100)^2 = 1200 × (10/100)^2 = Rs. 12.
73
What single discount is equivalent to two successive discounts of 25% and 60%?
Medium
ExplanationEquivalent discount = 100 − (100−25)(100−60)/100 = 70%.
74
What is 55% of 60% of 733?
Medium
Explanation55% of 60% of 733 = (55/100) × (60/100) × 733 = 241.89.
75
An interest rate rises from 12% to 19%. By how many percentage points did it increase?
Medium
ExplanationA percentage-point increase is a simple subtraction: 19% − 12% = 7 percentage points.
76
A value is first decreased by 6% and then increased by 95%. What is the overall net percentage change?
Medium
ExplanationStarting with 100: after the first change it becomes 94.00, and after the second change it becomes 183.30 — a net change of +83.3% from the original 100.
77
What is 25% of 113?
Medium
Explanation25% of 113 = (25/100) × 113 = 28.25.
78
What percent is 1/20?
Medium
Explanation1/20 × 100 = 5%.
79
What is 90% of 830?
Medium
Explanation90% of 830 = (90/100) × 830 = 747.
80
What single discount is equivalent to two successive discounts of 48% and 4%?
Medium
ExplanationEquivalent discount = 100 − (100−48)(100−4)/100 = 50.08%.
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81
A value is first increased by 12% and then decreased by 32%. What is the overall net percentage change?
Medium
ExplanationStarting with 100: after the first change it becomes 112.00, and after the second change it becomes 76.16 — a net change of -23.84% from the original 100.
82
A shop offers successive discounts of 48% and 60% on an item marked at Rs. 1125. What is the final selling price?
Medium
ExplanationFinal price = 1125 × (1 − 48/100) × (1 − 60/100) = Rs. 234.
83
A shop offers successive discounts of 5% and 36% on an item marked at Rs. 2625. What is the final selling price?
Medium
ExplanationFinal price = 2625 × (1 − 5/100) × (1 − 36/100) = Rs. 1596.
84
92 is what percent of 230?
Medium
Explanation(92 / 230) × 100 = 40%.
85
A value is first decreased by 28% and then decreased by 80%. What is the overall net percentage change?
Medium
ExplanationStarting with 100: after the first change it becomes 72.00, and after the second change it becomes 14.40 — a net change of -85.6% from the original 100.
86
An item is priced at Rs. 725 before tax. With a sales tax of 16%, what is the total price?
Medium
ExplanationTotal price = Price × (1 + 16/100) = 725 × 1.1600 = Rs. 841.
87
Rs. 7650 is invested at 10% simple interest per annum for 6 years. What is the total amount after 6 years?
Medium
ExplanationAmount = Principal + Interest = 7650 + 4590 = Rs. 12240.
88
A shopkeeper marks up an item costing Rs. 804 by 3%. What is the markup amount (in Rs.)?
Medium
ExplanationMarkup amount = CP × 3/100 = 804 × 0.0300 = Rs. 24.12.
89
What is 70% of 70% of 75?
Medium
Explanation70% of 70% of 75 = (70/100) × (70/100) × 75 = 36.75.
90
A shopkeeper marks up an item costing Rs. 1205 by 16%. What is the markup amount (in Rs.)?
Medium
ExplanationMarkup amount = CP × 16/100 = 1205 × 0.1600 = Rs. 192.8.
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91
A value is first increased by 35% and then decreased by 4%. What is the overall net percentage change?
Medium
ExplanationStarting with 100: after the first change it becomes 135.00, and after the second change it becomes 129.60 — a net change of +29.6% from the original 100.
92
What is 3% of 717?
Medium
Explanation3% of 717 = (3/100) × 717 = 21.51.
93
Rs. 12259 is invested at 3% simple interest per annum for 6 years. What is the total amount after 6 years?
Medium
ExplanationAmount = Principal + Interest = 12259 + 2206.62 = Rs. 14465.62.
94
Rs. 5935 is invested at 7% simple interest per annum for 6 years. What is the total amount after 6 years?
Medium
ExplanationAmount = Principal + Interest = 5935 + 2492.7 = Rs. 8427.7.
95
What is 4% of 303?
Medium
Explanation4% of 303 = (4/100) × 303 = 12.12.
96
A value is first increased by 32% and then decreased by 15%. What is the overall net percentage change?
Medium
ExplanationStarting with 100: after the first change it becomes 132.00, and after the second change it becomes 112.20 — a net change of +12.2% from the original 100.
97
An item marked at Rs. 990 is sold at a discount of 30%. What is the selling price?
Medium
ExplanationSelling price = Marked price × (1 − 30/100) = 990 × 0.7000 = Rs. 693.
98
A value is first decreased by 15% and then increased by 4%. What is the overall net percentage change?
Medium
ExplanationStarting with 100: after the first change it becomes 85.00, and after the second change it becomes 88.40 — a net change of -11.6% from the original 100.
99
What is 80% of 369?
Medium
Explanation80% of 369 = (80/100) × 369 = 295.2.
100
What is 50% of 257?
Medium
Explanation50% of 257 = (50/100) × 257 = 128.5.
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