Number Theory · Topic 7 of 9

🔢 Digit & Word Problems

2 exam question types, fully solved

The real skill here is translation: turn the words and digits into a small equation, then solve it.

The facts that crack digit problems

A two-digit number with tens digit t and units digit u equals 10t + u; its reverse is 10u + t.

• Difference of number and reverse = 9 × (t − u)

• Sum of number and reverse = 11 × (t + u)

Two numbers, sum S and difference D: larger = , smaller = . This avoids solving two equations every time.

🔄Two-Digit ReverserSee the 9× and 11× patterns

Tens digit (t)

Units digit (u)

Number

= 52

Reversed

= 25

Difference = 52 − 25 = 27 → 9 × (t − u) = 9 × 3 = 27 Sum = 52 + 25 = 77 → 11 × (t + u) = 11 × 7 = 77

A two-digit number and its reverse differ by 27, so the digit difference = 27 ÷ 9 = .

Q1A two-digit number and its reverse differ by 45. The difference of the digits is:

Q2The sum of two numbers is 40 and their difference is 8. The larger number is:

Q3A number is 5 times another, and their sum is 48. The smaller number is:

📚

Real exam questions — Digit & Word Problems

2 question types · 6 solved examples from real SSC papers

The skill here is translation: turn the words and digits into a small equation, then solve.

How to solve this type

Write a two-digit number as 10t + u, where t is the tens digit and u is the units digit. The reversed number is 10u + t. Their difference is 9(t − u) and their sum is 11(t + u). For "sum of all numbers formed by given digits", each digit sits in each place (n−1)! times, so add the digits, multiply by (n−1)!, then by 111…1.

When the digits of a two-digit number are reversed, the number decreases by 36. What is the difference of its digits?

A7B6C5D4

The sum of the digits of a two-digit number is 9. On reversing the digits, the new number is 27 more than the original. What is the units digit of the original number?

A3B6C7D4

Find the sum of all 3-digit numbers formed using the digits 2, 4 and 6, using each digit exactly once.

A2664B2440C2220D2886