Question
How many three-digit numbers are divisible by $9$?
✓
Answer
The two-digit numbers divisible by $9$ start from
$108, 117, 126, 135, ..., 999$
Here,
$a = 108$
$d = 9$
$a_n = a + (n - 1)d$
$\Rightarrow 999 = 108 + (n - 1)(9)$
$\Rightarrow 999 = 108 + 9n - 9$
$\Rightarrow 900 = 9n$
$\Rightarrow n = 100$
This, $100$ two-digit number are divisible by $9$.
$108, 117, 126, 135, ..., 999$
Here,
$a = 108$
$d = 9$
$a_n = a + (n - 1)d$
$\Rightarrow 999 = 108 + (n - 1)(9)$
$\Rightarrow 999 = 108 + 9n - 9$
$\Rightarrow 900 = 9n$
$\Rightarrow n = 100$
This, $100$ two-digit number are divisible by $9$.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Find the coordinates of the points which divide segment $A B$ into four equal parts, if $A (5,7)$ and $B (-3,-1)$
→Water in a canal, 5.4m wide and 1.8m deep, is flowing with a speed of 25km/hr. How much area can it irriggate in 40 minutes, if 10cm of standing water is required for irrigation?
Determine k so that (3k - 2), (4k - 6) and (k + 2) are three consecutive terms of an AP.
Solve the following quadratic equations by factorization:
$\frac{\text{x}+3}{\text{x}+2}=\frac{3\text{x}-7}{2\text{x}-3}$
→$\frac{\text{x}+3}{\text{x}+2}=\frac{3\text{x}-7}{2\text{x}-3}$
A toy is in the form of a hemisphere surmounted by a right circular cone of the same base radius as that of the hemisphere. If the radius of the base of the cone is 21cm and its volume is $\frac{2}{3}$ of the volume of hemisphere, calculate the height of the cone and the surface area of the toy.
→Sum of the squares of adjacent sides of a parallelogram is 130 sq.cm and length of one of its diagonals is14 cm. Find the length of the other diagonal.
The sum of the numerator and denominator of a fraction is 4 more than twice the numerator. If the numerator and denominator are increased by 3, they are in the ratio 2 : 3. Determine the fraction.
In the figures given below, an altitude is drawn to the hypotenuse by a right-angled triangle. The length of different line-segment are marked in figure. Determine $x, y, z$ in case.
→Answer the following questions based on the frequency polygon given in the adjacent figure.
(1) Write frequency of the class 50-60.
(2) State the class whose frequency is 14.
(3) State the class whose class mark is 55.
(4) Write the class in which the frequency is maximum.
(5) Write the classes whose frequencies are zero.
(1) Write frequency of the class 50-60.
(2) State the class whose frequency is 14.
(3) State the class whose class mark is 55.
(4) Write the class in which the frequency is maximum.
(5) Write the classes whose frequencies are zero.
Find the solution of the pair of equations $\frac{\text{x}}{10}+\frac{\text{y}}{5}-1=0$ and $\frac{\text{x}}{8}+\frac{\text{y}}{6}=15.$ Hence, find $\lambda,$ if $\text{y}=\lambda\text{x}+5.$
→