How many numbers lie between 10 and 300, which when divided by 4 leave a remainder 3

Solution:

The first number is 11, which divided by 4 leaves a remainder 3 between 10 and 300

The last term before 300 is 299, which is divided by 4 leave remainder 3.

So it is in an arithmetic progression as

11, 15, 19, 23, 299

First-term (a) = 11,

Common difference (d) = 15 - 11 = 4

We know that nth term,

a_n = a + (n - 1)d

Substituting the values

299 = 11 + (n - 1) 4

4(n - 1) = 288

So we get

(n - 1) = 72

n = 73

Therefore, 73 numbers lie between 10 and 300.

✦ Try This: How many numbers lie between 20 and 400, which when divided by 4 leave a remainder 2

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5

NCERT Exemplar Class 10 Maths Exercise 5.3 Problem 18

How many numbers lie between 10 and 300, which when divided by 4 leave a remainder 3

Summary:

73 numbers lie between 10 and 300, which when divided by 4 leave a remainder 3.

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