SSC CGL Percentage Questions with Detailed Solutions

Given:
Initial Value = 50000
Depreciation rates = 15%, 10%, 20%
Formula Used:
Final Value = Initial Value$$\times (1 - \frac{R_1}{100}) \times (1 - \frac{R_2}{100}) \times (1 - \frac{R_3}{100})$$​​
Solution:
​$$\text{Final Value} = 50000 \times (1 - 0.15) \times (1 - 0.10) \times (1 - 0.20)\\ \ \\\text{Final Value} = 50000 \times 0.85 \times 0.90 \times 0.80\\ \ \\\text{Final Value} = 50000 \times 0.612\\ \ \\\text{Final Value} = \bf30600$$​​
So the correct answer is (a).

Given:
Mistaken operation: Decrease by 10%
Correct operation: Increase by 10%
Formula Used:
Percentage difference = $$\frac{\text{Difference}}{\text{Correct Value}} \times 100$$​​
Solution:
Let the original value be 100.
The correct value should be: 100 + $$10\% \text{ of } 100$$​ = 110
The mistaken (final) value is: 100 - $$10\% \text{ of }$$​ 100 = 90
Difference between correct and mistaken value = 110 - 90 = 20
We need to find by what percent the final result (90) is less than the correct value (110).
​$$\text{Percentage less} = \frac{20}{110} \times 100\\ \ \\\text{Percentage less} = \frac{2}{11} \times 100 = \frac{200}{11}\\ \ \\\text{Percentage less} \approx 18.18\%$$​​
So the correct answer is (b).

Given:
Current Population = 44,100
Rate of increase = 5% annually
Time = 2 years ago
Formula Used:
A = $$P\times \left(1 + \frac{R}{100}\right)^{n}$$​​
Solution:
Let the population two years ago be P.
​$$44100 = P \times \left(1 + \frac{5}{100}\right)^{2}\\ \ \\44100 = P \times \left(\frac{105}{ 100}\right)^{2}\\ \ \\44100 = P \times \left(\frac{21}{20}\right)^{2}\\ \ \\44100 = P \times\left (\frac{441}{400}\right)\\ \ \\P = 44100 \times \left(\frac{441}{400}\right) = 40,000$$​​

So the correct answer is (a)

Given:
Initial Expenditure = 75% of Income
Income increase = 20%
Expenditure increase = 0%
Formula Used:
Savings = Income - Expenditure
Percentage increase = $$\frac{\text {Difference}}{\text {Original Value}} \times 100$$​​
Solution:
Assume the initial income is ₹100. Then expenditure is ₹75 and savings is ₹25
The new income is ₹120 (after a 20% increase).
The expenditure remains ₹75.
The new savings is 120 - 75 = ₹45
The increase in savings is 45 - 25 = ₹20
The percentage increase in savings is $$\frac{20} { 25} \times 100$$ =  80%
So the correct answer is (d).

Given:
Initial Ratio (Male : Female) = 4 : 3
Male increase = 15%
Female increase = 20%
Formula Used:
New value = Old value $$\times$$​ (100 + Increase)%
Solution:
Assume the initial number of males is 400 and females is 300 to simplify calculations.
Calculate the new male population after a 15% increase: 400 $$\times$$​ 1.15 = 460
Calculate the new female population after a 20% increase: 300 $$\times$$​ 1.20 = 360
The new ratio is 460 : 360 $$\implies$$​23 : 18
So the correct answer is (a)

​$$\textbf{Given:} \\ \space \, \\ \text{Total Qs} = 180 \\ \space \, \\ \text{Physics (40): } 75\% \text{ correct} = 30 \\ \space \, \\ \text{Chemistry (70): } 55\% \text{ correct} = 38.5 \\ \space \, \\ \text{Biology (70): } 45\% \text{ correct} = 31.5 \\ \space \, \\ \text{Passing} = 62\% \text{ of } 180 \\ \space \, \\ \textbf{Solution:} \\ \space \, \\ \text{Total correct answers} = 30 + 38.5 + 31.5 = 100 \\ \space \, \\ \text{Required passing marks} = 0.62 \times 180 = 111.6 \\ \space \, \\ \text{Shortfall} = 111.6 - 100 = 11.6 \\ \space \, \\ \textbf{Final Answer} \\ \space \, \\ 11.6$$​​

​$$\textbf{Given:} \\ \, \\\text{Height increased by } 60\% \\ \, \\\text{Base area remains same} \\ \, \\\textbf{Formula Used:} \\ \, \\\text{If a quantity increases by } a\%, \text{ then net increase } = a\% \\ \, \\\textbf{Solution:} \\ \, \\\text{Volume } = \text{Base Area} \times \text{Height} \\ \, \\\text{Base area is constant} \\ \, \\\text{Height increases by } 60\% \\ \, \\\text{Therefore volume also increases by } 60\% \\ \, \\\textbf{Final Answer:} \\ \, \\60\%$$​​

​$$\textbf{Given:}\\ \, \\\text{Employees} = 120\\ \, \\\text{Supervisors} = 15\\ \, \\\text{Employee kit} = 12\% \text{ of total employees}\\ \, \\\text{Supervisor kit} = 20\% \text{ of total employees}\\ \, \\\textbf{Formula Used:}\\ \, \\\text{Percentage value} = \frac{\text{Percentage}}{100} \times \text{Total}\\ \, \\\textbf{Solution:}\\ \, \\12\% \text{ of } 120 = 14.4\\ \, \\\text{Total employee items} = 120 \times 14.4 = 1728\\ \, \\20\% \text{ of } 120 = 24\\ \, \\\text{Total supervisor items} = 15 \times 24 = 360\\ \, \\\text{Total items} = 1728 + 360 = 2088\\ \, \\\textbf{Final Answer:}\\ \, \\2088$$​​

​$$\textbf{Given:}\\ \, \\\text{Liquid in container} = 4000 \text{ milliliters}\\ \, \\\text{Full capacity} = 0.008 \text{ kiloliters}\\ \, \\\textbf{Formula Used:}\\ \, \\\text{Percentage empty} = \frac{\text{Empty quantity}}{\text{Total capacity}} \times 100\\ \, \\\textbf{Solution:}\\ \, \\1 \text{ kiloliter} = 1000 \text{ liters}\\ \, \\0.008 \times 1000 = 8 \text{ liters}\\ \, \\8 \text{ liters} = 8000 \text{ milliliters}\\ \, \\\text{Empty quantity} = 8000 - 4000 = 4000\\ \, \\\text{Percentage empty} = \frac{4000}{8000} \times 100 = 50\%\\ \, \\\textbf{Final Answer:}\\ \, \\50\%$$​​

​$$\textbf{Given:}\\\ \, \\\text{Total students}=150\\\ \, \\\text{Cricket and Badminton}=30\\\ \, \\\text{Cricket only}=50\\\ \, \\\text{Badminton only}=40\\\ \, \\\text{Neither}=30\\\ \, \\\textbf{Formula Used:}\\\ \, \\\text{Total playing a sport}=\text{Only}+\text{Both}\\\ \, \\\textbf{Solution:}\\\ \, \\\text{Cricket players}=50+30=80\\\ \, \\\text{Badminton players}=40+30=70\\\ \, \\\text{Ratio}=80:70=8:7\\\ \, \\\textbf{Final Answer:}\\\ \, \\8:7$$​​

​$$\textbf{Given:}\\\ \, \\\text{Ratio of raw materials : wages : maintenance }=4:3:3\\\ \, \\\text{Increase in raw materials }=12\%\\\ \, \\\text{Increase in wages }=8\%\\\ \, \\\text{Decrease in maintenance }=10\%\\\ \, \\\textbf{Formula Used:}\\\ \, \\\text{Net percentage change}=\frac{\sum(\text{Ratio}\times\text{Percentage change})}{\sum\text{Ratios}}\\\ \, \\\textbf{Solution:}\\\ \, \\\text{Total ratio }=4+3+3=10\\\ \, \\(4\times12)+(3\times8)+(3\times(-10))\\\ \, \\=48+24-30=42\\\ \, \\\text{Overall change}=\frac{42}{10}=4.2\%\\\ \, \\\textbf{Final Answer:}\\\ \, \\4.2\%\ \text{increase}$$​​

​$$\textbf{Given:}\\\ \, \\\text{Total employed}=40000\\\ \, \\\text{Decrease in men}=4\%\\\ \, \\\text{Increase in women}=12\%\\\ \, \\\text{New total}=40480\\\ \, \\\textbf{Formula Used:}\\\ \, \\\text{New value}=\text{Original value}\left(1\pm\frac{\text{Percentage}}{100}\right)\\\ \, \\\textbf{Solution:}\\\ \, \\\text{Let number of men}=x\\\ \, \\\text{Then women}=40000-x\\\ \, \\0.96x+1.12(40000-x)=40480\\\ \, \\0.96x+44800-1.12x=40480\\\ \, \\-0.16x=-4320\\\ \, \\x=\frac{4320}{0.16}=27000\\\ \, \\\textbf{Final Answer:}\\\ \, \\27000$$

Exam Hall Method: 

​$$\textbf{Given:} \\\ \, \\\text{Commission on laptops} = 3\% \\\ \, \\\text{Price of one laptop} = 40,000 \\\ \, \\\text{Laptops sold per week} = 4 \\\ \, \\\text{Commission on printers} = 8\% \\\ \, \\\text{Price of one printer} = 8,000 \\\ \, \\\text{Printers sold per week} = 10 \\\ \, \\\text{Number of weeks} = 5 \\\ \, \\\textbf{Formula Used:} \\\ \, \\\text{Commission} = \frac{\text{Rate}}{100} \times \text{Selling Price} \\\ \, \\\textbf{Solution:} \\\ \, \\\text{Commission on one laptop} = \frac{3}{100} \times 40,000 = 1,200 \\\ \, \\\text{Commission on 4 laptops} = 4 \times 1,200 = 4,800 \\\ \, \\\text{Commission on one printer} = \frac{8}{100} \times 8,000 = 640 \\\ \, \\\text{Commission on 10 printers} = 10 \times 640 = 6,400 \\\ \, \\\text{Total commission per week} = 4,800 + 6,400 = 11,200 \\\ \, \\\text{Total commission for 5 weeks} = 5 \times 11,200 \\\ \, \\= 56,000 \\\ \, \\\textbf{Final Answer} \\\ \, \\\text{₹}56,000\$$​​

​$$\textbf{Given:} \\\ \, \\\text{Increase in radius} = 8\% \\\ \, \\\textbf{Formula Used:} \\\ \, \\\text{Net \% change} = x + y + \frac{xy}{100} \\\ \, \\\textbf{Solution:} \\\ \, \\\text{Area} \propto r^2 \\\ \, \\x = 8,\ y = 8 \\\ \, \\\text{Net \% increase} = 8 + 8 + \frac{8 \times 8}{100} \\\ \, \\= 16 + 0.64 \\\ \, \\= 16.64\% \\\ \, \\\textbf{Final Answer} \\\ \, \\16.64\%$$​​

​$$\textbf{Given:} \\\ \, \\\text{Expenditure ratio (groceries : rent : others)} = 3 : 5 : 2 \\\ \, \\\text{Increase in groceries} = 8\% \\\ \, \\\text{Increase in rent} = 4\% \\\ \, \\\text{Decrease in other expenses} = 10\% \\\ \, \\\textbf{Formula Used:} \\\ \, \\\text{Overall \% change} = \frac{\sum (\text{Ratio} \times \text{\% change})}{\sum \text{Ratios}} \\\ \, \\\textbf{Solution:} \\\ \, \\\text{Total ratio} = 3 + 5 + 2 = 10 \\\ \, \\\text{Weighted change} = (3 \times 8) + (5 \times 4) + (2 \times -10) \\\ \, \\= 24 + 20 - 20 \\\ \, \\= 24 \\\ \, \\\text{Overall percentage change} = \frac{24}{10} \\\ \, \\= 2.4\% \\\ \, \\\textbf{Final Answer} \\\ \, \\2.4\%\ \text{increase}$$​​