Question

The expenses of carpeting a half of the floor were 759 but if the length had been 6 m less than it was
the expenses would have been Rs. 561. What is the length?
(a) 21 m
(c) 45 m
(b) 23 m
(d) 27 m
​

Answer 1

Given:

The original expense of carpeting half of the floor $=Rs. 759$

The expense of carpeting half of the floor when its length was 6m less $=Rs. 561$

To Find:

What is the actual length of the floor?

Solution:

Let 'x' be the length and 'y' be the breadth of the floor.

Now,

For 1st case,

cost per  ${{\text{m}}^{2}}\times \left( \frac{xy}{2} \right)=759.........(\text{i})$

For 2nd case,

cost per  ${{\text{m}}^{2}}\times \left( \frac{\left( x-6 \right)\times y}{2} \right)=561.........(\text{ii})$

Then,

Dividing equation (i) by equation (ii), we get,

$\frac{x}{x-6}=\frac{759}{561}$

$\Rightarrow 561x=759\left( x-6 \right)$

$\Rightarrow 561x=759x-4554$

$\Rightarrow 4554=759x-561x$

$\Rightarrow 198x=4554$

$\Rightarrow x=\frac{4554}{198}$

$\therefore x=23$

Hence, the required length of the floor is 23m.