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.
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