Q11 of 85 Page 110

A ladder has rungs 25 cm apart. The rungs decrease uniformly from 60 cm at bottom to 40 cm at top. If the distance between the top rung and the bottom rung is 2.5 in, find the length of the wood required.

The distance between 2 consecutive rungs is 25cm and the distance between the top and bottom rung is 2.5m = 250cm.


∴ no. Of rungs = + 1 = 11


The length of the bottom rung is 60cm and going upwards the length of the rung decreases uniformly.


The length of last rung is 40cm.


So, the length of the rung will form a finite AP.


With first term a = 60(T1) and the last 11th term as 40(T11)


Now, d =


=


=


⇒ d= – 2


the length of the wood required is given by S11


we know that, Sn = × (2a + (n – 1)d)


So, S11 = × (2a + (n – 1)d)


⇒ S11 = × (2(60) + (11 – 1)( – 2))


⇒ S11 = × ( 120 – 20)


⇒ S11 = × 100


⇒ S11 = 550


∴ the length of the wood required is 550cm i.e. 5.5m.


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