Class 10 Math All topics Arithmetic Progressions

A ladder has rungs $25$ cm. apart. The rungs decrease uniformly in the length from $45$ cm. at the bottom to $25$ cm. at the top. If the top and the bottom rungs are $221 $m apart, what is the length of the wood required for the rungs

(a)

$280$ cm

(b)

$320$ cm

(c)

$250$ cm

(d)

$385$ cm

Correct answer: (d)

Solution: The distance between the top and the bottom rungs $=221 $ m $=250$ cm and the distance between two consecutive rungs $=25$ cm.

Therefore, the number of gaps between the rungs $=25250 =10$.

So, the total number of rungs in the ladder $=11$

The length of the bottom rung is $45$ cm and the lengths of rungs decrease uniformly from bottom to top.

Therefore, the numbers involved in the lengths (in cm) of the rungs from bottom to top form an AP with $a=45,l=25$ and $n=$ total number of rungs $=11$.

$=211 (45+25)$

$=211 ×70$

$=11×35=385$

Hence, the length of the wood required for rungs $=385$ cm.

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