**In this post, we will discuss how to solve number system questions that are asked on two digit numbers from number system for SBI PO, IBPS PO and SSC CGL Exams.**

Number system is one of the fundamental topics in the quantitative aptitude section of SBI PO, IBPS PO and SSC CGL Exams. Number system is a system to represent numbers using digits and symbols. Number system provides a unique representation of every number and represents arithmetic and algebraic structure of the figures. The knowledge of Number system helps us perform various calculations and operations while solving number system questions on two digit number that are often asked in IBPS PO and SSC CGL Exam.

In our previous post - Number System I - What is Number System and What are the Different Types of Numbers in Number System? we have discussed what is number system and the different types of numbers in the number system. In this post, we will discuss questions on two digit numbers and solve them using smart methods which will help you save time in IBPS PO and SSC CGL Exam.

**Module 1: Number System Questions on two digit numbers**

Suppose there is a two digit number ‘ab’, it can be represented as a x 10 and b x 1 as 'a' is in tens place and 'b' is in units place.

Likewise, if there is a three digit number ‘abc,” it can be represented as a x 100, b x 10 and c x 1 as 'a' is in hundreds place, 'b' is in tens place and 'c' is in units place.

Likewise, if there is a three digit number ‘abc,” it can be represented as a x 100, b x 10 and c x 1 as 'a' is in hundreds place, 'b' is in tens place and 'c' is in units place.

**Example 1: Number System Questions on two digit numbers**

**Question:**The number obtained by interchanging a two-digit number is 27 more than the original number. If the sum of the two digits is 13, what is the original number?

1) 63 2)74 3)85 4)58 5) None of the above.

**Regular Method:**

**Solution:**

**Step 1:**

Let us assume the original number to be as ab = 10a + b

Let us assume the interchanged number to be as ba = 10b + a

**Step 2:**

In the question it is mentioned that the number obtained by interchanging the digits is 27 more than the original number.

10b + a = 10a + b + 27

10b + a = 10a + b + 27

9b – 9a = 27

b – a = 3 (i)

**Step 3:**

As mentioned in the question the sum of two digits is 13 i.e.

a + b = 13 (ii)

**Step 4:**

Now add the equation 1 and equation 2 we get,

2b = 16

b = 8

b = 8

**Step 5:**

Let’s substitute the b’s value in equation 1

a + 8 = 13

a = 5

ab = 58

Therefore, the original number is 58.

**Smart Method**

**Solution:**

**Step 1:**

In this smart method of finding the two digit number, we need to first take the conditions into consideration.

As it is given in the question that a + b = 13

We can add the digits in the given options and check whether the options satisfy our condition or not.

Option 1; 63 = 6 + 3 = 9; this option doesn’t satisfy our condition as the sum of the digit is not 13

Option 2; 74 = 7 + 4 = 11; this option doesn’t satisfy our condition as the sum of the digit is not 13

Option 3; 85 = 8 + 5 = 13; this option satisfies our condition as the sum of the digit is 13

Option 4; 58 = 5 + 8 = 13; this option satisfies our condition as the sum of the digit is 13

**Step 2:**

As option 3 and 4 satisfies our condition, we can take the second condition ba = ab + 27 given in the question to verify which option is the correct option.

Option 3; 85 => 58; 58 is not equal to 85 + 27, therefore we eliminate this option.

Option 4; 58 => 85; 85 is equal to 58 + 27, therefore this is the correct answer.

Therefore, the correct answer is option 4; 58.

**Example 2:**

**Questions on two digit number from number system**

**Question:**When the digits of a two-digit number are interchanged, the number obtained is less than the original number by 36. What is the original number if the difference of the two digits is 4?

1) 84 2)51 3)73 4) Cannot be determined 5) None of these

**Smart Method**

**Solution:**

**Step 1:**

Let us assume the original number to be as ab = 10a + b

Let us assume the interchanged number to be as ba = 10b + a

As it is mentioned in the question that the interchanged number is less than 36 by the original number

10b + a = 10a + b – 36 (i)

**Step 2:**

The second condition given in the question is that the difference between the two digits of the original number is 4,

a– b = 4 (ii)

**Step 3:**

We can subtract the digits in the given options and check whether the options satisfy our condition or not.

Option 1; 84 = 8 - 4 = 4; this option satisfies our condition as the difference between the digit is 4.

Option 2; 51 = 5 -1 = 4; this option satisfies our condition as the difference between the digit is 4.

Option 3; 73= 7 - 3 = 4; this option satisfies our condition as the difference between the digit is 4.

**Step 4:**

As option 1,2 and 3 satisfies our condition, we can take the first condition

10b + a = 10a + b – 36 given in the question to verify which option is correct.

10b + a = 10a + b – 36 given in the question to verify which option is correct.

Option 1; 84 = 48; 48 = 84 - 36, therefore we can take this option into consideration.

Option 2; 51 = 15; 15 = 51 - 36, therefore this option can be taken into consideration.

Option 3; 73 = 37; 37 = 73 - 36, therefore this option can be taken into consideration.

As all the three options are correct and satisfy our condition we cannot determine the answer.

Therefore, the correct answer is option 4; cannot be determined.

###
**Number System Questions on two digit numbers for practice**

**Question:**The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?

1) 3 2) 4 3) 9 4) Cannot be determined 5) None of These

**Question:**The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1:2?

1) 4 2) 8 3) 16 4) 19 5) None of These

Do leave your answers in the comment section!

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