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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 $2 \frac{1}{2}$ m apart, what is the length of the wood required for the rungs?

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280

320

250

385

answer is D.

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Detailed Solution

Given, the distance between the top and bottom rungs of a ladder

= 2 \frac{1}{2}

= 250

cm.
The distance between two adjacent rungs

= 25

cm.
⇒ The number of gaps between the rungs

= \frac{250}{25}

= 10

⇒ The total number of rungs on the ladder

= 11

.
The bottom rung is 45 cm long, and the lengths of the rungs decrease uniformly from bottom to top.
The formed AP has

a = 45

l = 25

, and

n = 11

.
We know,

S_{n} = \frac{n}{2} (a + l)

⇒

S_{11} = \frac{11}{2} (45 + 25)

⇒

S_{11}

= \frac{11}{2} \times 70

⇒

S_{11}

= 11 \times 35 = 385

Therefore, the length of wood required for rungs

= 385

cm.
Hence, the correct option is 4.

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