The ratio of Students : teachers : administrators = 1500 : 50 : 5.
The new ratio of Students : teachers : administrators = 1800 : new teachers : new administrators
Given the ratios are maintained.
i.e., they are proportional.
∴  \(\frac { 1500 }{ 1800 } =\frac { 50 }{ New\quad teachers } =\frac { 5 }{ New\quad admins } \)
From the first two ratios, taking, cross product
\(\frac { 1500 }{ 1800 } =\frac { 50 }{ New\quad teachers } \)
New Teachers \(\times\) 1500 = 50 \(\times\) 1800
New Teacher = \(\frac { 50\times 1800 }{ 1500 } \)
New Teacher = 60
Also \(\frac { 1500 }{ 1800 } =\frac { 5 }{ New(admin) } \)
New admins \(\times\) 1500 = 5 \(\times\) 1800
New admms = \(\frac { 5\times 1800 }{ 1500 } \) = 6
∴ For 1800 students 60 teachers and 6 administrators are needed.

In 40 minutes, electricity used = 3 units.
In 1 minute, electricity used =\(3\over 40\) units.
In 120 minutes (2 hours), electricity used = \({3\over 40} \times\)120 = 9 units
Thus, the heater consumed 9 units of electricity in 2 hours.

\(1:2=\frac{1}{2}\)
\(2:1=\frac{2}{1}\times\frac{2}{2}=\frac{4}{2}\)
Here \(\frac{4}{2}\) larger than \(\frac{1}{2}\)
\(\therefore\) 2 : 1 larger than 1: 2

\(4:5=\frac{4}{5}\times\frac{3}{3}=\frac{12}{15}\)
\(8:15=\frac{8}{15}\)
Here \(\frac{12}{15}\) larger than \(\frac{8}{15}\) and 4: 5 is larger than 8: 15

Total number of students = 50.
Number of boys = 30.
Then number of girls = 50 - 30 = 20.
(i) Ratio of number of boys to no. of girls = \(\frac { 30 }{ 20 } \)
\(=\frac { 30\div 10 }{ 20\div 10 } =\frac { 3 }{ 2 } =3:2\)
(ii) \(\frac { Number\ of\ girls }{ Total\ number\ of\ students } =\frac { 20 }{ 50 } =\frac { 20\div 10 }{ 50\div 10 } =\frac { 2 }{ 5 } =2:5\)
(iii) \(\frac { Number\ of\ boys }{ Total\ number\ of\ students } =\frac { 30 }{ 50 } =\frac { 30\div 10 }{ 50\div 10 } =\frac { 3 }{ 5 } =3\ :\ 5\)