Question

A ladder has rungs 25 cm apart. The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top. If the top and bottom rungs are 2.5 metre apart, what is the length of the wood required for the rungs?

• A. 2 metres
• B. 3.5 metres
• C. 9 metres
• D. 12.5 metres

Answer 1

The correct option is B 3.5 metres

It is given that the rugs are 25 cm apart and the top and bottom rugs are 2.5m arpart.
$\therefore Totalnumberofrugs=\frac{2.5\times 100}{20}+1=\frac{250}{25}+1=11$
Now as the length of the rugs decreases uniformly, they will be in an A.P
The length of the wood required for the rugs equals the sum of all the $s_n=\frac{n}{2}(a+l)$

First term, a = 45 and Last term, l = 25 and n = 11
$\therefore S_{10}=\frac{11}{2}(45+25)=\frac{11}{2}\left(70\right)=385cm$
$\therefore$ The length of the wood required for the rugs is $385cm$