Question
How many two digit numbers are divisible by 3?
✓
Answer
Two digits numbers divisible by 3 are
$
12,15,18,21, \ldots, 99
$
Here, $a=13, d=15-12=3$ and $I =99$
Let number divisible by 3 and $n$
$
\begin{aligned}
& \therefore T_n=1=a+(n-1) d \\
& 99=12+(n-1) \times 3 \\
& \Rightarrow 99-12=3(n-1) \\
& \Rightarrow 3(n-1)=87 \\
& \Rightarrow n-1=\frac{87}{3}=29 \\
& \therefore n=29+1 \\
& =30 .
\end{aligned}
$
$
12,15,18,21, \ldots, 99
$
Here, $a=13, d=15-12=3$ and $I =99$
Let number divisible by 3 and $n$
$
\begin{aligned}
& \therefore T_n=1=a+(n-1) d \\
& 99=12+(n-1) \times 3 \\
& \Rightarrow 99-12=3(n-1) \\
& \Rightarrow 3(n-1)=87 \\
& \Rightarrow n-1=\frac{87}{3}=29 \\
& \therefore n=29+1 \\
& =30 .
\end{aligned}
$
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
The model of a building is constructed with scale factor $1:30$.
(i) If the height of the model is $80\ cm$, find the actual height of the building in metres.
(ii) If the actual volume of a tank at the top of the building is $27\ m^3$, find the volume of the tank on the top of the model.
→(i) If the height of the model is $80\ cm$, find the actual height of the building in metres.
(ii) If the actual volume of a tank at the top of the building is $27\ m^3$, find the volume of the tank on the top of the model.
The line through $P (5, 3)$ intersects y-axis at $Q.$
write the equation of the line
→write the equation of the line
In the following figures, the line of symmetry has been drawn with a dotted line. Identify the corresponding sides and the corresponding angles about the line of symmetry.
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
$x^2+ 5x + 15 = 0.$
→$x^2+ 5x + 15 = 0.$
In the given below figure,
∠ BAD = 65°
∠ ABD = 70°
∠ BDC = 45°
Find: (i) ∠ BCD, (ii) ∠ ADB.
Hence show that AC is a diameter.
∠ BAD = 65°
∠ ABD = 70°
∠ BDC = 45°
Find: (i) ∠ BCD, (ii) ∠ ADB.
Hence show that AC is a diameter.
In each of the following find the values of k of which the given value is a solution of the given equation:
$k x^2+\sqrt{2} x-4=0 ; x=\sqrt{2}$
→$k x^2+\sqrt{2} x-4=0 ; x=\sqrt{2}$
Find the compounded ratio of the following:
$3 : 5, 7 : 9$ and $15 : 28$
→$3 : 5, 7 : 9$ and $15 : 28$
Mamta invested Rs. 10,846 in buying the shares of a company at Rs. 17 each. If the face value of each share be? 10 and company paid 15% dividend at the end of the year, find the dividend earned by her.
Two dice $($each bearing numbers $1$ to $6)$ are rolled together. Find the probability that the sum of the numbers on the upper$-$most faces of two dice is: $7, 8$ or $9$
→Find the mean, median and mode of the following marks obtained by $16$ students in a class test marked out of $10$ marks.
$0, 0, 2, 2, 3, 3, 3, 4, 5, 5, 5, 5, 6, 6, 7$ and $8.$
→$0, 0, 2, 2, 3, 3, 3, 4, 5, 5, 5, 5, 6, 6, 7$ and $8.$