A ladder has rungs 25cm apart .The rungs decreas uniformly in lenght from 45cm at the bottom to 25cm at the top.If the top and the bottom rungs are 2 &1/2 m apart ,what is the lenght of the wood required for the rungs?

from-NCERT book (optional question)

I do not know from where to start,please give me the explanation.It is urgent.

hmmmm....

start:

find the number of rungs.....in 2.5 metres.....

we'll have 0 + (n-1)25 = 250----> 11 rungs.....

the bottom most rung is 45cms long..top most....25cms...

so we've an ap here!

last term=25

first term=45

n=11

total length = sum of lengths of rungs = sum of ap...

= 11/2 (70)

 = 385cms

3.85m

cheers!

no of rungs=250cm/25cm=10 rungs

we need to find the total amt of wood used

this is equal to lenght of first rung + length of second rung............+ length of 10th rung

we apply the formula of sum of  10 terms=n/2(first term + last term)

thus 10/2(25+45)

5(70)

=350cm     or 3.5m  is the total amt of wood required

PLS CORRECT IF WRONG

@rahul---there are 11 rungs......not 10...

it is an ap here too.............

let the lower rung be at 0cm

so u have a rung evry 25cms.....

0,25,50,........250.

so first term here is  0

last term  250 cms

number of terms or rungs = (250 - 0)/25   +  1

                                               = 11

so u have 2 aps in this q-

cheers!

I think rahul is correct:

Lenght of wood required for rungs

=Sum of 10 terms of an A.P with the first term 45cm and the last term 25 cm.

@rahul....cammon think properly.....

i told m assuming that loewer rung is at 0cm level.....

sheeeeesh!

wat is prob 10 or 20 cms above grnd level for u is 0 cm for me...(dat s ma assumption)---m doin this so that i can get this 250cms diff into the pic......

awryt ill start frm scratch!(again):--for both rahul nd rudra!

0 - 24.99999999.... cms ---1 rung

25--49.99999999 cms--1 rung

50--74.99999999 cms --1 rung

75-99.999999 cms 1 rung

100-124.99999999 --1 rung

125--149.9999999 -- 1 rung

150--174.999999--1 rng

175--199.999999 -- 1 rung

200--224.999999--1 rung

225--249.999999 cms --1 rung

at 250 th cm-----(2 1/2 m frm base--0cm ) anothr rung.....

jus count the number of rungs! = 11

if u dont get it now--- i giv up!!!

Please download and see:

how many tyms to tell u.......

0 cm is not grnd level....m assumin that the lowest rung is at 0 cm level......

so the grnd is at sum negative cm level........similar to assumin ZERO POTENTIAL LINE in phy in energy conservation......it is a reference standard.....dats it!

grnd level isnt ma concern here---the difference of 250 cms alone matters!

if u assume the lowest rung to be at 25 cms level then final rung will b at 275 cms level------difference=250 cms

u r counting the length from GROUND LEVEL and m countin FROM THE LOWEST RUNG.....the length from ground to lower rung doesnt matter to me!!!!!!!!

sum1 help me out --- eithr m not explainin properly or theyr not gettin it !!!

sum1 xplain ma steps!

@vasanth if you look at it practically everyone would want to minimise the amt of wood used as it is profitable allthemore it wont EVER be used as pointed out by rudra in the post above.thus according to me thereshould be 10 rungs

look at the diagram below from NCERT (q no 3)

@ vasanth

Your explanaion is clear to me.

Let me try putting it in another way: 

In the question it says ' from 45cm at the bottom ' which can mean that the lowest rung of the ladder may or may not be at the ground level.

Lets  say x cm above ground there is a rung which is the bottom rung. Then the topmost rung is x + 2.5 metres above the ground.

so x + (n-1) 25 = x + 250

so n = 11

I hope now your doubts are clear.

What if we consider the lowest rung is at 25 cm above the ground level?

The last rung is at 250 cm (from the lowest rung).

So 25+(n-1)25=250

then n=10..??????