Rs.12000

135°

Initial population = 5,50,000
Increased population = 6,05,000
∴ Increase in population = 6,05,000 - 5,50,000
= 55,000
∴ Per cent Increase = \({55,000\over 5,50,000}\times100\%=10\%\)

We have
\(115\%={115\times{1\over 100}}={115\over100}=1.15\)
Thus, 115% = 1.15

We have \(40\%=40\times{1\over 100}\)
\(={40\over 100}={2\over 5}\)    (∵ HCF of 40 and 100 is 20)
Thus 40% = 2 : 5

Principal = Rs.56,000
Time = 2 years
Interest =  Rs.280 p.a.
Let rate of interest be x
\(\therefore R=\frac { 100I }{ P\times T } \)
\(x=\frac { 100\times 280 }{ 56000\times 2 } \)
\(\Rightarrow \quad x=\frac { 1 }{ 4 } \)
\(\therefore \) x=0.25%
Hence, rate of interest for 2 years = 0.25%

Total parts =3+1=4
Percentage of 1st part=\(\frac { 3 }{ 4 } \times 100\)
=3X 25
=75%
percentage of 2nd part=\(\frac { 1 }{ 4 } \times 100\)
=1X25
=25%

C.P=Rs.240
Profit=10%
S.P=?
\(\therefore \) profit =\(\frac { 10 }{ 100 } \times 240\)=Rs.24
\(\Rightarrow \)S.P=C.Profit
=240+24
=Rs.264

Since, 3a=2b
\(\Rightarrow \) \(\frac { a }{ b } =\frac { 2 }{ 3 } \)
and 6b=5c
\(\Rightarrow \)\(\frac { b }{ c } =\frac { 5 }{ 6 } \)
\(\therefore \quad \frac { a }{ b } \times \frac { b }{ c } =\frac { 2 }{ 3 } \times \frac { 5 }{ 6 } \)
\(\Rightarrow \)\(\frac { a }{ c } =\frac { 5 }{ 9 } \)
a:c = 5:9

Total number of students is 32 and 4 are absent
\(\therefore\) Percentage of absent students
\({4\over32}\times 100\%={1\over8}\times100\%=125\%\)

Fractions of the ratio 2 : 5 and 3 : 7 are \({2\over5}\)and \(3\over7\) respectiveIy
Now, \({2\over5}\times{7\over7}={14\over35}\Rightarrow {3\over7}\times{5\over5}={15\over35}\)
Both fractions have same denominator but numerator is not equal i.e.14 < 15.
So, \({3\over7}>{2\over5}\)
Hence, the given ratios is not equivalent.

Given, 0.064
\(\therefore 0.064\times {100\over100}={64\over1000}\times100\%={64\over10}\%=6.4\%\)

Rs.4050, Rs.6750

Rs.100

40% gain