Maths Exercise
Number System
10 Practice Questions
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1) Which fraction is the smallest: 7/8, 7/9, 4/5, 5/7?
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- a) 7/8
- b) 7/9
- c) 4/5
- d) 5/7
Compare decimal values or cross‑multiply: 7/9 ≈ 0.777…, 5/7 ≈ 0.714…, 4/5 = 0.8, 7/8 = 0.875. Smallest is 5/7.
2) The cube of 997 is close to which value?
▶
- a) 991,026,973
- b) 991,092,673
- c) 991,027,273
- d) 991,029,773
Use (1000−3)³ = 1000³ − 3×1000²×3 + 3×1000×3² − 3³ = 1,000,000,000 − 9,000,000 + 27,000 − 27 ≈ 991,027,000. Accurate value is 991,027,273.
3) A number divided by 899 leaves remainder 63. Dividing the same number by 29, remainder?
▶
- a) 10
- b) 5
- c) 4
- d) 2
Since 899 = 29×31, N = 899k + 63. Then N mod 29 = 63 mod 29 = 5.
4) If d is a digit (0–9), what is the remainder when (9d − 11) is divided by 8?
▶
- a) 0
- b) 1
- c) 3
- d) 7
Treat d as a digit. (9d − 11) mod 8 depends on d. Note 90 − 11 = 79 ≡ 7 (mod 8); each +10 in 9d adds +2 (mod 8). Try d = 0–9 and observe the cycle; pick the option matching the remainder.
5) 495 − 1 is exactly divisible by?
▶
- a) 48
- b) 50
- c) 29
- d) 98
Use an − 1 is divisible by a − 1. With a = 49, the expression is divisible by 48. Also by factors of (49 − 1) = 48, i.e., 2, 3, 4, 6, 8, 12, 16, 24, 48.
6) If 5432e is divisible by 9, what is digit e?
▶
- a) 4
- b) 5
- c) 6
- d) 9
Sum of digits 5+4+3+2+e = 14+e must be multiple of 9 → e = 4.
7) A tank holds 135 L. One‑fourth is full. What part when it contains 80 L?
▶
- a) 2/3
- b) 16/27
- c) 5/9
- d) 3/8
Fraction filled = 80/135 = 16/27.
8) What is two‑third of half of 369?
▶
- a) 123
- b) 246
- c) 271⅜
- d) 184.5
Half of 369 is 184.5; two‑third of that is 123.
9) 5/7 of a number exceeds 1/7 of the same number by 10. The number?
▶
- a) 25
- b) 150
- c) 17.5
- d) 175
(5/7 − 1/7)N = 10 → (4/7)N = 10 → N = 17.5.
10) In a class, 3/5 students are girls; rest are boys. If 2/5 of girls and 1/6 of boys are absent, what fraction are present?
▶
- a) 52/75
- b) 51/75
- c) 2/3
- d) 7/10
Girls present: (1 − 2/5)×3/5 = 3/5×3/5 = 9/25. Boys share: 2/5; present = (1 − 1/6)×2/5 = 5/6×2/5 = 1/3. Total present = 9/25 + 1/3 = 27/75 + 25/75 = 52/75.
Unitary Method
10 Practice Questions
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1) If 15 pens cost ₹180, what is the cost of 8 pens?
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- a) ₹90
- b) ₹96
- c) ₹104
- d) ₹112
Cost per pen = ₹180 ÷ 15 = ₹12. Cost of 8 pens = 8 × ₹12 = ₹96.
2) A car travels 450 km in 9 hours. How far will it travel in 5 hours at the same speed?
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- a) 200 km
- b) 225 km
- c) 250 km
- d) 275 km
Speed = 450 ÷ 9 = 50 km/h. Distance in 5 h = 50 × 5 = 250 km.
3) If 12 workers can build a wall in 48 hours, how many workers are needed to build the same wall in 18 hours?
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- a) 24
- b) 28
- c) 32
- d) 36
Work = workers × hours. Required workers = (12 × 48) ÷ 18 = 32.
4) The weight of 7 identical containers is 56 kg. What is the weight of 15 such containers?
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- a) 105 kg
- b) 120 kg
- c) 135 kg
- d) 150 kg
Weight per container = 56 ÷ 7 = 8 kg. For 15: 15 × 8 = 120 kg.
5) A garrison of 500 men had provisions for 24 days. A reinforcement of 300 men arrives. For how many days will the food last now?
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- a) 15 days
- b) 16 days
- c) 17.5 days
- d) 18 days
Total man‑days = 500 × 24 = 12,000. With 800 men: 12,000 ÷ 800 = 15 days.
6) If a machine prints 1,200 pages in 30 minutes, how many pages can it print in 12 minutes?
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- a) 400
- b) 480
- c) 520
- d) 600
Rate = 1,200 ÷ 30 = 40 pages/min. In 12 min: 40 × 12 = 480 pages.
7) 10 pipes can fill a tank in 24 minutes. How long will it take to fill the tank if 2 pipes go out of order?
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- a) 28 minutes
- b) 30 minutes
- c) 32 minutes
- d) 35 minutes
Time ∝ 1/number of pipes. With 8 pipes: 24 × (10 ÷ 8) = 30 minutes.
8) If the cost of 2 dozen bananas is ₹120, find the cost of 18 bananas.
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- a) ₹80
- b) ₹90
- c) ₹100
- d) ₹110
24 bananas cost ₹120 → ₹5 each. 18 bananas cost 18 × ₹5 = ₹90.
9) 15 men can complete a work in 20 days. In how many days can 25 men complete the same work?
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- a) 10 days
- b) 12 days
- c) 14 days
- d) 16 days
Man‑days = 15 × 20 = 300. Days = 300 ÷ 25 = 12.
10) A map scale: 2 cm represents 50 km. If the distance between two cities on the map is 7 cm, what is the actual distance?
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- a) 150 km
- b) 175 km
- c) 200 km
- d) 225 km
Per cm = 50 ÷ 2 = 25 km. Actual distance = 7 × 25 = 175 km.
Power, Indices and Surd
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Simplification
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Miscellaneous
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Algebra
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LCM and HCF
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Percentage
20 Practice Questions
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1) What is 20% of 150?
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- a) 20
- b) 25
- c) 30
- d) 35
20% of 150 = (20/100) × 150 = 30.
2) What is 15% of 800?
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- a) 90
- b) 100
- c) 120
- d) 140
15% of 800 = (15/100) × 800 = 120.
3) A price increases by 10% from ₹500. What is the new price?
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- a) ₹520
- b) ₹550
- c) ₹600
- d) ₹650
Increase = 10% of 500 = ₹50 → New price = ₹550.
4) Decrease ₹900 by 25%. What is the result?
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- a) ₹675
- b) ₹700
- c) ₹725
- d) ₹750
25% of 900 = 225 → 900 − 225 = ₹675.
5) Increase a number by 20% then decrease by 20%. Net change?
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- a) −4%
- b) −2%
- c) 0%
- d) +4%
Let 100 → after +20% = 120 → after −20% = 96 → net change = −4%.
6) 40% of a class are girls. If girls = 30, what is total strength?
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- a) 60
- b) 70
- c) 75
- d) 80
30 = 40% → Total = 30 ÷ 0.40 = 75.
7) 45 is what percent of 180?
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- a) 20%
- b) 25%
- c) 30%
- d) 35%
Percent = (45/180)×100 = 25%.
8) Bought at ₹400, sold at ₹460. Profit percent?
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- a) 10%
- b) 12%
- c) 15%
- d) 20%
Profit = 60 → (60/400)×100 = 15%.
9) Marked price ₹800, discount 12.5%. Selling price?
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- a) ₹690
- b) ₹700
- c) ₹720
- d) ₹740
12.5% of 800 = 100 → SP = 800 − 100 = ₹700.
10) Increase from 72 to 90. Percentage increase?
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- a) 20%
- b) 25%
- c) 30%
- d) 35%
Increase = 18; percent = (18/72)×100 = 25%.
11) If x% of 200 = 50, find x.
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- a) 20%
- b) 25%
- c) 30%
- d) 35%
x% × 200 = 50 → x = (50/200)×100 = 25%.
12) Express 0.35 as a percentage.
▶
- a) 3.5%
- b) 35%
- c) 350%
- d) 0.35%
0.35 × 100% = 35%.
13) A student scores 36 out of 50. Percentage?
▶
- a) 68%
- b) 70%
- c) 72%
- d) 75%
(36/50)×100 = 72%.
14) Salary ₹25,000 increased by 12%. New salary?
▶
- a) ₹27,500
- b) ₹28,000
- c) ₹28,500
- d) ₹29,000
12% of 25,000 = 3,000 → New salary = ₹28,000.
15) Population decreases by 10% from 50,000 then increases by 10%. Final population?
▶
- a) 49,500
- b) 50,000
- c) 50,500
- d) 51,000
50,000 → 45,000 → 49,500.
16) Change from 240 to 180. Percentage decrease?
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- a) 20% decrease
- b) 25% decrease
- c) 33% decrease
- d) 50% decrease
Decrease = 60; percent = (60/240)×100 = 25% decrease.
17) One number is 25% more than another. What is the ratio (bigger:smaller)?
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- a) 4:5
- b) 5:4
- c) 6:5
- d) 3:2
Let smaller = 4k → bigger = 4k + 25% of 4k = 5k → ratio = 5:4.
18) GST 18% on item price ₹1,250. What is the bill total?
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- a) ₹1,450
- b) ₹1,470
- c) ₹1,475
- d) ₹1,500
GST = 18% of 1,250 = ₹225 → Total = ₹1,475.
19) A tank is 80% full. Capacity is 1,200 L. How many litres to fill it?
▶
- a) 200 L
- b) 220 L
- c) 240 L
- d) 260 L
Remaining = 20% of 1,200 = 240 L.
20) 15% of a number is 75. What is the number?
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- a) 450
- b) 480
- c) 500
- d) 520
Number = 75 ÷ 0.15 = 500.
Profit and Loss
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Discount
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Trigonometry
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Height and Distance
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Geometry and Co-ordinate
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Average
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Ratio and Proportion
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Partnership
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Mixture and Alligation
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Simple Interest
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Compound Interest
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Time and Work
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Pipe and Cistern
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Mensuration
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Time, Distance and Train
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Boat and Stream
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Statistics and Data Interpretation (D.I.)
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