NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.2 Question 13
NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.2 Question 13
Question:
How many three-digit numbers are divisible by 7?
Given:
Three-digit numbers.
To Find:
The number of three-digit numbers divisible by 7.
Formula:
The number of multiples of i between a and b is given by \( \frac{m}{i} - \frac{n}{i} + 1\) where
m ≤ b and n ≥ a and are divisible by i.
Solution:
The smallest three-digit number is 100.
The largest three-digit number is 999.
Therefore a = 100 and b = 999.
Since we have to find numbers divisible by 7, i = 7
We need to find the number of multiples of 7 between 100 and 999 (inclusive).
999 is not divisible by 7. 994 is the next smallest number divisible by 7.
100 is not divisible by 7. 105 is the next greatest number divisible by 7.
Using the formula,
⇒ The number of three-digit numbers = \( \frac{994}{7} - \frac{105}{7}+ 1 \) ⇒ The number of three-digit numbers = 142 - 15 + 1
⇒ The number of three-digit numbers = 128
Result:
There are 128 three-digit numbers divisible by 7.
Next question solution:
NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.2 Question 14
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