- Percentage
- Profit & Loss
- Ratio & Proportion
- Simple Interest/Compound Interest
- Time, Speed & Distance
- Time & Work
- Average
- Mixture & Alligation
- Number System
- HCF and LCM
- Simplification
1.
Q: Find 20% of 250.
Solution:
20%20\% of 250 = (20/100)×250=50(20/100) \times 250 = 50
✅ Answer: 50
2.
Q: A shopkeeper gains 20% on selling an item for ₹600. Find the cost price.
Solution:
SP = ₹600, Gain = 20%
CP=SP1+gain100=6001.2=500\text{CP} = \dfrac{SP}{1+\dfrac{gain}{100}} = \dfrac{600}{1.2} = 500
✅ Answer: ₹500
3.
Q: Divide ₹480 between A and B in the ratio 5:3.
Solution:
Sum of ratio = 5 + 3 = 8
A’s share = (5/8)×480=300(5/8) \times 480 = 300
B’s share = (3/8)×480=180(3/8) \times 480 = 180
✅ Answer: ₹300 and ₹180
4.
Q: Find simple interest on ₹5000 at 8% p.a. for 2 years.
Solution:
SI = P×R×T100=5000×8×2100=800\dfrac{P \times R \times T}{100} = \dfrac{5000 \times 8 \times 2}{100} = 800
✅ Answer: ₹800
5.
Q: A car travels 300 km at a speed of 60 km/h. Find the time taken.
Solution:
Time = Distance/Speed = 300/60=5300/60 = 5 hours
✅ Answer: 5 hours
6.
Q: A can complete a work in 20 days and B in 30 days. How many days will they take together?
Solution:
Work/day = 1/20+1/30=(3+2)/60=5/60=1/121/20 + 1/30 = (3+2)/60 = 5/60 = 1/12
Thus, time = 12 days
✅ Answer: 12 days
7.
Q: Find the average of 12, 15, 21, and 30.
Solution:
Sum = 78
Average = 78/4=19.578/4 = 19.5
✅ Answer: 19.5
8.
Q: In what ratio must 40% alcohol and 70% alcohol be mixed to obtain 50% alcohol?
Solution (Alligation method):
(70−50):(50−40)=20:10=2:1(70-50):(50-40) = 20:10 = 2:1
✅ Answer: 2:1
9.
Q: Find the smallest number divisible by 12, 15, and 18.
Solution:
LCM of 12,15,18 = 180
✅ Answer: 180
10.
Q: Simplify: 15%15\% of 360 + 25%25\% of 280
Solution:
= 54+70=12454 + 70 = 124
✅ Answer: 124
11.
Q: 34+56=?\dfrac{3}{4} + \dfrac{5}{6} = ?
Solution:
LCM of 4 and 6 = 12\text{LCM of 4 and 6 = 12}
(9+10)/12=19/12(9+10)/12 = 19/12
✅ Answer: 1912\dfrac{19}{12} or 17121\frac{7}{12}
12.
Q: Find the HCF of 36 and 48.
Solution:
HCF = 12
✅ Answer: 12
13.
Q: Find the value of (75)2−(25)2(75)^2 – (25)^2.
Solution:
Use a2−b2=(a+b)(a−b)a^2 – b^2 = (a+b)(a-b)
(75+25)(75−25)=100×50=5000(75+25)(75-25) = 100 \times 50 = 5000
✅ Answer: 5000
14.
Q: A train of length 180m crosses a pole in 15 seconds. Find its speed.
Solution:
Speed = Distance/Time = 180/15=12180/15 = 12 m/s = 12×18/5=43.212 \times 18/5 = 43.2 km/h
✅ Answer: 43.2 km/h
15.
Q: Find the selling price to gain 25% if CP = ₹1600.
Solution:
SP = 1600×(1+0.25)=1600×1.25=20001600 \times (1+0.25) = 1600 \times 1.25 = 2000
✅ Answer: ₹2000
16.
Q: Find the compound interest on ₹2000 at 10% p.a. for 2 years (compounded annually).
Solution:
CI = 2000×(1.1)2−2000=2000×1.21−2000=2420−2000=4202000 \times (1.1)^2 – 2000 = 2000 \times 1.21 – 2000 = 2420 – 2000 = 420
✅ Answer: ₹420
17.
Q: The sum of two numbers is 60, and their difference is 20. Find the numbers.
Solution:
Let numbers = x and y, where x > y
x+y=60x+y=60 and x−y=20x-y=20
Adding: 2x=80⇒x=40,y=202x = 80 \Rightarrow x = 40, y=20
✅ Answer: 40 and 20
18.
Q: 8 workers can complete a work in 15 days. How many workers are needed to complete it in 10 days?
Solution:
Workers×Days=Constant\text{Workers} \times \text{Days} = \text{Constant}
8×15=x×108 \times 15 = x \times 10
x=12x = 12
✅ Answer: 12 workers
19.
Q: Find the value of 1225\sqrt{1225}.
Solution:
1225=35\sqrt{1225} = 35
✅ Answer: 35
20.
Q: A man loses 12% in selling an article for ₹704. Find cost price.
Solution:
CP=SP1−loss100=7040.88=800\text{CP} = \dfrac{SP}{1 – \dfrac{loss}{100}} = \dfrac{704}{0.88} = 800
✅ Answer: ₹800
21.
Q: 25 is what percent of 200?
Solution:
25200×100=12.5%\dfrac{25}{200} \times 100 = 12.5\%
✅ Answer: 12.5%
22.
Q: Find the next number: 2, 6, 12, 20, 30, ?
Solution:
Pattern: n2+nn^2 + n
Next term = 62+6=426^2 + 6 = 42
✅ Answer: 42
23.
Q: If the perimeter of a square is 64 cm, find the area.
Solution:
Side = 64/4=1664/4 = 16 cm
Area = 162=25616^2 = 256 cm²
✅ Answer: 256 cm²
24.
Q: Find the mean of first 5 prime numbers.
Solution:
First 5 primes = 2, 3, 5, 7, 11
Mean = (2+3+5+7+11)/5=28/5=5.6(2+3+5+7+11)/5 = 28/5 = 5.6
✅ Answer: 5.6
25.
Q: A shopkeeper marks his goods 30% above cost price and allows a discount of 10%. Find his profit percent.
Solution:
Net gain = 30−10−(30×10)/100=17%30-10-(30 \times 10)/100 = 17\%
✅ Answer: 17%
26.
Q: Find the smallest 4-digit number divisible by 8.
Solution:
1000 ÷ 8 = 125 → 8 × 125 = 1000
✅ Answer: 1000
27.
Q: If 5x + 3 = 18, find x.
Solution:
5x=15⇒x=35x = 15 \Rightarrow x = 3
✅ Answer: 3
28.
Q: (4)3×(4)2=?(4)^3 \times (4)^2 = ?
Solution:
43+2=45=10244^{3+2} = 4^5 = 1024
✅ Answer: 1024
29.
Q: If a: b = 2:3 and b:c = 4:5, find a:c.
Solution:
b is common: LCM of 3 and 4 is 12
Thus, a:b = 8:12, b:c = 12:15
Thus, a:c = 8:15
✅ Answer: 8:15
30.
Q: What is 3/5 of 500?
Solution:
3/5×500=3003/5 \times 500 = 300
✅ Answer: 300
31.
Q: Find 7.5% of 400.
Solution:
(7.5/100)×400=30(7.5/100) \times 400 = 30
✅ Answer: 30
32.
Q: Find the ratio of 45 minutes to 2 hours.
Solution:
45:120=3:845:120 = 3:8
✅ Answer: 3:8
33.
Q: If a boat covers 60 km downstream in 3 hours and returns in 4 hours, find the speed of the stream.
Solution:
Downstream speed = 20 km/h, Upstream speed = 15 km/h
Speed of stream = (20−15)/2=2.5(20-15)/2 = 2.5 km/h
✅ Answer: 2.5 km/h
34.
Q: Simplify: 33×323^3 \times 3^2
Solution:
33+2=35=2433^{3+2} = 3^5 = 243
✅ Answer: 243
35.
Q: Find the sum of first 10 natural numbers.
Solution:
Sum = n(n+1)/2=10×11/2=55n(n+1)/2 = 10 \times 11/2 = 55
✅ Answer: 55
36.
Q: What is the average of first 6 multiples of 7?
Solution:
Multiples = 7, 14, 21, 28, 35, 42
Sum = 147
Average = 147/6=24.5147/6 = 24.5
✅ Answer: 24.5
37.
Q: Find the LCM of 8 and 14.
Solution:
LCM = 56
✅ Answer: 56
38.
Q: If 20% of x = 80, find x.
Solution:
x=80×(100/20)=400x = 80 \times (100/20) = 400
✅ Answer: 400
39.
Q: Find the square of 95.
Solution:
952=902595^2 = 9025
✅ Answer: 9025
40.
Q: 1/4 of a number is 5 more than 1/6 of the number. Find the number.
Solution:
Let number = x
x/4=x/6+5x/4 = x/6 +5
Multiply by 12:
3x=2x+60⇒x=603x = 2x + 60 \Rightarrow x=60
✅ Answer: 60
41.
Q: Find the compound interest on ₹5000 for 2 years at 5% p.a.
Solution:
CI = 5000×(1.05)2−5000=5525−5000=5255000 \times (1.05)^2 – 5000 = 5525 – 5000 = 525
✅ Answer: ₹525
42.
Q: A man’s salary is increased by 20% and then again by 10%. Find the total percentage increase.
Solution:
Total % = 20+10+(20×10)/100=32%20 + 10 + (20\times10)/100 = 32\%
✅ Answer: 32%
43.
Q: Find the area of a rectangle of length 12 m and breadth 8 m.
Solution:
Area = 12×8=9612 \times 8 = 96 m²
✅ Answer: 96 m²
44.
Q: A sells an article at 10% loss. If SP is ₹540, find CP.
Solution:
CP=SP/0.9=540/0.9=600CP = SP/0.9 = 540/0.9 = 600
✅ Answer: ₹600
45.
Q: Find the number whose 20% is 36.
Solution:
Number = 36×(100/20)=18036\times (100/20) = 180
✅ Answer: 180
46.
Q: If 2 pencils cost ₹6, what is the cost of 15 pencils?
Solution:
Cost of 1 pencil = ₹3
Thus, 15 pencils = ₹45
✅ Answer: ₹45
47.
Q: Find 625\sqrt{625}.
Solution:
625=25\sqrt{625} = 25
✅ Answer: 25
48.
Q: The sum of three consecutive even numbers is 222. Find the numbers.
Solution:
Let numbers = x, x+2, x+4
x+x+2+x+4=222⇒3x+6=222⇒x=72x+x+2+x+4=222 \Rightarrow 3x+6=222 \Rightarrow x=72
Thus, numbers = 72, 74, 76
✅ Answer: 72, 74, 76
49.
Q: Find simple interest on ₹6000 at 6% for 4 years.
Solution:
SI = 6000×6×4/100=14406000\times6\times4/100 = 1440
✅ Answer: ₹1440
50.
Q: Find the speed of a train which travels 90 km in 2 hours 30 minutes.
Solution:
Time = 2.5 hours
Speed = 90/2.5=3690/2.5 = 36 km/h
✅ Answer: 36 km/h
