Download App

Arithmetic Progressions — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsArithmetic Progressions3 Marks
Question
A ladder has rungs $25$ cm apart. The rungs decrease uniformly in length from $45$ cm at the bottom to $25$ cm at the top. If the top and bottom rungs are $2\frac 12$m apart, what is the length of the wood required for the rungs?
[Hint: Number of rungs = $\frac{250}{25} + 1$]
Image
✓

Answer

It is given that the gap between two consecutive rungs is 25 cm and the top and bottom rungs are 2.5 metre i.e., 250 cm apart.
$\therefore$ Number of rungs = $\frac { 250 } { 25 } $+ 1 = 10 + 1 = 11.
It is given that the rungs are decreasing uniformly in length from 45 cm at the bottom to 25 cm at the top.
Therefore, lengths of the rungs form an A.P. with first term a = 45 cm and $11^{th}$​​​​​​​ term l = 25 cm. n = 11
$\therefore$ Length of the wood required for rungs = Sum of 11 terms of an A.P. with first term 45 cm and last term is 25 cm
$= \frac { 11 } { 2 }$ ( 45 + 25 ) cm $\left[ \because S _ { n } = \frac { n } { 2 } ( a + l ) \right]$
$= \frac { 11 } { 2 }$(70) cm
$= 11 (35) cm$
$= 385 cm$
Length of the wood required for rungs = $\frac{385}{100}$ = 3.85 metres ($\because$100 cm = 1 m)
The length of the wood required for the rungs is 3.85 metres.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Arithmetic Progressions→Arithmetic Progressions — all question types→Maths STD 10 question papers→CBSE Board STD 10 question papers→CBSE Board question paper generator→

Similar questions

Find the value of k for which the following system of equations has no solution:
$kx - 5y = 2$
$6x + 2y = 7$
→
The slant height of a frustum of a cone is $4 \ cm$ and the perimeters of its circular ends are $18 \ cm$ and $6 \ cm .$ Find the curved surface area of the frustum.
→
Cards marked with numbers 1, 3, 5, ..., 101 are placed in a bag and mixed thoroughly. A card is drawn at random from the bag. Find the probability that the number on the drawn card is:
  1. Less than 19.
  2. A prime number less than 20.
→
Find the median of the following data:
Marks20-3030-4040-5050-6060-7070-8080-90
Number of Students51525207810
→
Prove the following trigonometric identities.
If $\cos\text{A}+\cos^2\text{A}=1,$ prove that $\sin^2\text{A}+\sin^4\text{A}=1.$
→
The perimeter of a certain sector of a circle of radius 5.6m is 27.2m. Find the area of the sector.
→
Find $\text{HCF}$ and $\text{LCM}$ of $180,252$ and $324.$
→
State the two properties which are necessary for given two triangles to be similar.
→
If the area of an equilateral triangle is $81\sqrt{3}\text{cm}^2,$ find its height.
→
The perimeter of a rectangular plot of land is 80m and its breadth is 16m. Find the length and area of the plot.
→