It costs Rs. 6000/- and Rs. 6,100- respectively to paint the 4 walls of 2 square halls, of the same height. If the length of one hall exceeds the length of the other by 1 m and the cost of painting is Rs. 5 per sq.m., what is the height of the two walls ?

let the length of the halls be 'a' and 'a+1' m respectively and height of the halls be 'h' m.

Area of 4 walls of first square hall (A1) = $$(4\times a\times h) m^2$$

Given, cost of painting is Rs. 5 per sq.m

$$\Rightarrow$$  cost of painting 4 walls of the first square hall = A1 * 5 = $$4\times a\times h\times 5 = Rs. 20*a*h$$.

Given that this cost of painting = Rs. 6000

$$\Rightarrow$$ 20*a*h = 6000...........(1)

Similarly,

Area of 4 walls of second square hall (A2) = $$(4\times a+1\times h) m^2$$

$$\Rightarrow$$  cost of painting 4 walls of the second square hall = A2 * 5 = $$4\times a+1\times h\times 5 = Rs. 20*(a+1)*h$$.

Given that this cost of painting = Rs. 6100

$$\Rightarrow$$ 20*(a+1)*h = 6100............(2)

Dividing (2) with (1), we get

$$\frac{a+1}{a} = \frac{6100}{6000}$$

$$\Rightarrow 1 + \frac{1}{a} = \frac{61}{60}$$

$$\Rightarrow a = 60$$

Substituting this value in equation (1), we get

20*60*h = 6000

$$\Rightarrow$$ h = 5 m.

So, the height of the two walls is 5 m.