$$\eqalign{ & {\text{Population after two years}}, \cr & = 5000 \times {\left[ {1 + {\frac{2}{{100}}} } \right]^2} \cr & = 5202 \cr & {\text{Alternatively}}, \cr & 5000 = = 2\% \uparrow \Rightarrow 5100 = = 2\% \uparrow \Rightarrow 5202 \cr} $$

Men × Time = Work 100 × 1 = 100 unit work 150 × 1 = 150 unit work Extra man power = 50 But since, new workers are $$\frac{5}{4}$$ time as efficient as existing workers Thus, Actual no. of workers = $$\frac{{50}}{{\frac{5}{4}}}$$ = 40 workers % required = $$\frac{{40 \times 100}}{{100}} = 40\% $$

$$\eqalign{ & \frac{{ {ax} }}{{100}} = \frac{{ {by} }}{{100}} \cr & or,\,ax = by \cr & \Rightarrow y = \frac{{ {ax} }}{b} \cr & c\% \,{\text{of}}\,y = \frac{{ {cy} }}{{100}} \cr & or,\,\frac{{ {cy} }}{{100}} = \frac{{ {cax} }}{{100b}} \cr & {\text{Thus}}, \cr & c\% \,{\text{of}}\,y = \frac{{ca}}{b}\% \,{\text{of}}\,x \cr} $$

$$\eqalign{ & {\text{Let the number of total workers}} = x \cr & {\text{Number of skilled workers}} \cr & = 75\% \,of\,x = \frac{{75x}}{{100}} = \frac{{3x}}{4} \cr & {\text{No}}{\text{. of unskilled workers}} \cr & = 25\% \,of\,x = \frac{{25x}}{{100}} = \frac{x}{4} \cr & {\text{No}}{\text{. of permanent workers}}, \cr & = {\frac{{80}}{{100}}} \times {\frac{{3x}}{4}} + {\frac{{20}}{{100}}} \times {\frac{x}{4}} \cr & = {\frac{{3x}}{5}} + {\frac{x}{{20}}} \cr & = \frac{{13x}}{{20}} \cr & {\text{No}}{\text{.}}\,{\text{of}}\,{\text{temporary}}\,{\text{workers,}} \cr & = x - {\frac{{13x}}{{20}}} = \frac{{7x}}{{20}} \cr & {\text{Now}}, \cr & \frac{{7x}}{{20}} = 126 \cr & x = 360 \cr} $$

$$\eqalign{ & \frac{{\text{P}}}{{100 + {\text{P}}}} = \frac{{\text{Q}}}{{100}} \cr & {\text{or}},\,100\left( {{\text{P}} - {\text{Q}}} \right) = {\text{PQ}} \cr & {\text{or}},\,\left( {{\text{P}} - {\text{Q}}} \right) = \frac{{{\text{PQ}}}}{{100}} \cr} $$

Let there are X books in the library. Number of Hindi books = 60% of X = $$\frac{{60{\text{X}}}}{{100}}$$  = 0.6X Remaining Books = X - 0.6X = 0.4X Number English books = 40% of reaming books = 60% of 0.4X = 0.24X. Urdu Books = X-0.6X -0.24X = 0.16X Given, 0.24X = 3600 X $$ = \frac{{3600}}{{0.24}} = 15000$$ Urdu Books = 0.16X = 0.16 × 15000 = 2400

Total number of cubes = 160 + 56 = 216 Thus, side of cube = 6 unit No. of cubes without exposure = (6 - 2)3 = 64 Thus 64 cubes will be inside of a big cube Now, rest cubes = 160 - 64 = 96 No. of cubes with one face outside = 6 × (4 × 4) = 96 Required % = $$\frac{{90 \times 100}}{{216}} = 44.44\% $$

They covered the distance in this way together in different hours 6 + 6.5 + 7 + 7.5 + 8 + 8.5 + 9 + 9.5 + 10 = 72 Means,they'll meet at the 9th hr. So, In that time A will cover = 4 × 9 = 36kmThey will meet in Midway

Quantity of water in 250 kg dry grapes, $$ = \frac{{10}}{{100}} \times 250 = 25\,{\text{kg}}$$ Then, pulp of grapes = 225 kg We get 20 kg pulp in 100 kg fresh grapes. To get 225 kg pulp , we need fresh grapes,$${\text{ = }}\frac{{100 \times 225}}{{20}} = 1125\,{\text{kg}}$$

Let the no. of total student in the class = 100 and number of boy = X and 12% of the 100 is 12
Number of girl is x - 12
total number of student is x + (x - 12) = 100
therefore x = 56.
Then, No of boys = 56 No. of girls = 44 Boys : Girls = 56 : 44 = 14 : 11

Let the number of bushes originally be 100 Number of bushes after one year 100 ==10% (↑) ==> 110 After second year it becomes 110 ==8%(↑) ==> 118.8 After third year, 118.8 ==8%(↓)==> 109.3 Now, according to the question 109.3 = 26730 1 = $$\frac{{26730}}{{109.3}}$$ So, 100 = $$\frac{{26730}}{{109.3}} \times 100$$    = 25000
Thus, number of bushes originally was 25000 NOTE:You can take number of bushes originally as x then solve for the x

Total number of passenger in each compartment = $$\frac{{ {25 \times 7} }}{5}$$  = $$35$$
Total berth = 352 = 1225
Maximum available capacity
$$\eqalign{ & = \frac{{ {1225 \times 80} }}{{100}} \cr & = 980\,{\text{seats}} \cr} $$

Let the number of candidates appearing from each state be X. Then, 7% of X - 6% of X = 80 Or, 1% of X = 80 Or, X = 80 × 100 X = 8000

After first discount, 100 ---- 8%↓ ----> 92 After second discount, 92 ---- 12%↓ ----> 80.96 Single discount = 100 - 80.96 = 19.04%

Let the basic salaries of A and B be x and y respectively.
Now,
$$\eqalign{ & x + 65\% \,\,{\text{of }}x = y + 80\% \,\,{\text{of }}y \cr & \Rightarrow x + \frac{{ {65x} }}{{100}} = y + \frac{{ {80y} }}{{100}} \cr & \Rightarrow \frac{x}{y} = \frac{{180}}{{165}} \cr & \Rightarrow x:y = 12:11 \cr} $$

$$\eqalign{ & {\text{Total number all three got together is}}, \cr & = {1136 + 7636 + 11628} \cr & = 20400 \cr & \% {\text{ of vote the winning candidate got is}}, \cr & = {\frac{{11628}}{{20400}}} \times 100 \cr & = 57\% \cr} $$

Let his original salary be Rs. 100 Salary after increment = Rs. 120 Let the tax on original salary be 20% and now tax on increased salary (Rs. 20) will be 22% i.e. Rs. 4.40 Thus, increase in tax liability $$ = \frac{{4.40}}{{20}} \times 100 = 22\% $$

$$\eqalign{ & {\text{Quantity of salt in 6L of sea water,}} \cr & = \frac{{ {6 \times 4} }}{{100}} = 0.24 \cr & {\text{Percentage of salt in 5L of sea water,}} \cr & = \frac{{ {0.24 \times 100} }}{5} = 4\frac{4}{5}\% \cr} $$

$$\eqalign{ & 78\% \,{\text{of}}\,\,750 + 34\% \,{\text{of}}\,x = 30\% \,{\text{of}}\,\,2630 \cr & or,\, {\frac{{ {78 \times 750} }}{{100}}} + \frac{{34x}}{{100}} = \left( {30 \times 2630} \right) \times 100 \cr & or,\,78 \times 750 + 34x = 30 \times 2630 \cr & or,\,34x = 78900 - 58500 \cr & or,\,x = \frac{{20400}}{{34}} \cr & {\text{Hence}},\,x = 600 \cr} $$

No. of population who are literate = 50% of 296000 = 148000 No. of male = 166000 No. of female = 296000 - 166000 = 130000 No. of literate male = 70% of 166000 = 116200 No. of literate women
= 148000 - 116200 = 31800