# Problems on Digits and Numbers

We will learn how to solve different types of problems on digits and numbers.

1. Numbers 1, 2, 3, 4, ........., 98, 99, 100 are multiplied together. The number of zeros at the end of the product on the right will be equal to

(a) 24

(b) 21

(c) 22

(d) 13

Solution:

The value of the ‘n’ = 100.

Therefore, number of zeros at the end of 1 × 2 × 3 × 4 × 5 × .............. × 99 × 100

= (100 ÷ 5) + (100 ÷ 5^2)

= 20 + 4

= 24

Note: Number of zeros at the end of the product of natural numbers = n/5 + n/5^2 + n/5^3 + ........... (upto n terms)

2. How many three digit natural numbers are possible?

(a) 999

(b) 990

(c) 890

(d) 900

Solution:

Number of three digit numbers = 9 × 10^(3 - 1) = 9 × 10^2 = 900

Note: Number of numbers with specific number of digits = 9 × 10^(d - 1), where ‘d’ = number of digits.

3. The difference of the squares of two nos. is 135 & their difference is 5. The product of the numbers is

(a) 182

(b) 178

(c) 180

(d) 176

Solution: Let, two numbers be ‘a’ and ‘b’

According to the problem,

a - b = 5 and a^2 - b^2 = 135

Therefore, a + b = 135 ÷ 5 = 27

Since, a = (27 + 5) ÷ 2 = 16 and b = 16 - 5 = 11

Therefore, required value of ab = 16 × 11 = 176

4. The sum of x and y is three times their difference. Find the ratio of x and y:

(a) 2 : 1

(b) 2 : 3

(c) 3 : 4

(d) 4 : 3

Solution:

a + b = 3(a - b)

or, 2a = 4b

Therefore, a : b = 4 : 2 = 2 : 1

5. The sum of the two numbers m and n is 5760, & the difference is one-third of the greater number. Which is the greater number?

(a) 3450

(b) 3456

(c) 3475

(d) 3500

Solution:

Let, two numbers be x and y.

Now according to the problem,

x/3 = x - y

or, 3x - 3y = x

or, 2y = 3y

or, x :  y = 3 : 2

Therefore, the greatest number = 5760 × 3/(3 + 2) =5760 × 3/5 = 3456