A ladder has rungs 25 cms …

It is given that the gap between two consecutive rungs is 25 cm and the top and bottom rungs are 2.5 metre i.e., 250 cm apart.
{tex}\therefore{/tex}  Number of rungs = {tex}\frac { 250 } { 25 } {/tex}+ 1 =  10 + 1 = 11.
It is given that the rungs are decreasing uniformly in length from 45 cm at the bottom to 25 cm at the top.
Therefore, lengths of the rungs form an A.P. with first term a = 45 cm and 11^th term l = 25 cm. n = 11
{tex}\therefore{/tex}  Length of the wood required for rungs = Sum of 11 terms of an A.P. with first term 45 cm and last term is 25 cm
{tex}= \frac { 11 } { 2 }{/tex} ( 45 + 25 ) cm {tex}\left[ \because S _ { n } = \frac { n } { 2 } ( a + l ) \right]{/tex}
{tex}= \frac { 11 } { 2 }{/tex}(70) cm
= 11 (35) cm
= 385 cm
Length of the wood required for rungs = {tex}\frac{385}{100}{/tex} = 3.85 metres ({tex}\because{/tex}100 cm = 1 m)
The length of the wood required for the rungs is 3.85 metres.