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

**1.** The number of digits used in numbering each page of a book of 150 pages is

(a) 342

(b) 348

(c) 328

(d) 322

Solution:

Required number of digits = (9 × 1) + (90 × 2) + (150 - 99) × 3

= 9 + 180 + 153

= 342

Answer: (a)

**Note:** Number of 1
digit numbers = 9

Number of 2 digit numbers = 90

**2.** If the digits
of a two-digit number are interchanged, the number so formed is 18 more than
the original number. The sum of digits is 8. What is the thrice value of
original number?

(a) 159

(b) 78

(c) 105

(d) None

Solution:

Let, the unit’s and ten’s digit be ‘a’ and ‘b’ respectively.

Therefore, a + b = 8 and a - b = 18 ÷ 9 = 2

Since, a = (8 + 2) ÷ 2 = 5 and b = 5 - 2= 3

Therefore, the required value is 3 × 35 = 105

Answer: (c)

**3.** A two-digit
number is eight times the sum of its digits. If 45 is subtracted from the
numbers, the position of digits get interchanged. The number is:

(a) 56

(b) 83

(c) 72

(d) None

Solution:

Two digits differ by = 45 ÷ 9 = 5 and the number is divisible by 8.

Now according the options,

The required number is 72

Answer: (c)

**Note:** The
difference of a two digit number and the number obtained by writing it in
reverse order is equal to nine times of difference of digits.

**4.** Find the total
numbers of three-digit numbers, which are exactly divisible by six?

(a) 340

(b) 126

(c) 190

(d) 150

Solution:

Total number of 3-digit numbers from 100 to 999 is 900.

Therefore, the least 3-digit number divisible by 6 is 6 × 17 = 102 and greatest number is 6 × 166 = 996

Therefore, required number of numbers = 166 - 17 + 1 = 150

Answer: (d)

**5.** A mathematics book
containing 20 pages. One sheet is missing among them. Sum of the page numbers
of the remaining pages of the mathematics book is 195. The numbers written on
both the sides of the missing sheet of the mathematics book must be

(a) 9, 10

(b) 11, 12

(c) 5, 6

(d) 7, 8

Solution:

Sum of the page numbers of the book = 1 + 2 + 3 + ................ + 19 + 20 = (20 × 21)/2 = 210

The sum of page numbers of missing sheet = 210 - 195 = 15 = (7 + 8)

Therefore, required page number of missing sheet = 7 and 8.

Answer: (d)

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