A ladder has rungs 25 , cm apart. (see Figure | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The rungs are placed at a distance of $25 \, cm$ from each other. The total distance between the top and bottom rung is $2 \frac{1}{2} \, m = 250

Vedclass · Accepted Answer

$385$

Vedclass · Answer

(D) The rungs are placed at a distance of $25 \, cm$ from each other. The total distance between the top and bottom rung is $2 \frac{1}{2} \, m = 250 \, cm$.The number of gaps between the rungs is $\frac{250}{25} = 10$.Since there is a rung at both ends,the total number of rungs $n$ is $10 + 1 = 11$.As the lengths of the rungs decrease uniformly,they form an Arithmetic Progression $(A.P.)$.The first term $a = 45 \, cm$ and the last term $l = 25 \, cm$.The total length of the wood required is the sum of the $A.P.$ series,given by the formula $S_n = \frac{n}{2}(a + l)$.Substituting the values: $S_{11} = \frac{11}{2}(45 + 25) = \frac{11}{2}(70) = 11 	imes 35 = 385 \, cm$.Thus,the total length of wood required for the rungs is $385 \, cm$.

$A$ ladder has rungs $25 \, cm$ apart. (see Figure). The rungs decrease uniformly in 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?

Similar Questions

Find the sum given below: $7 + 10 \frac{1}{2} + 14 + \ldots + 84$

Find the sum of the series: $7 + 10 \frac{1}{2} + 14 + \ldots + 84$.

In an $AP$,if $a = 1$,$a_{n} = 20$,and $S_{n} = 399$,then $n$ is:

The famous mathematician associated with finding the sum of the first $100$ natural numbers is

For an $A.P.$,the first term is $10$ and the $10^{th}$ term is $100$. Then,the sum of the first $10$ terms is..........

Vedclass Test Series

Exam Paper Generator

Online Exam Module