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# Find the answer to each question\begin{align} & \text{a) The sum of face value and place value of 9 in 691 is} \\ & \text{b) Arun interchanges the hundreds and tens digits of the number 673}\text{.} \\ & \text{ By how much is the number increased}\text{.} \\ & \text{c)}\text{ Find the next number in the sequence 5, 8, 11, 14, 17}.... \\ & \text{d) How many even number are there between 40 and 60 }\text{.} \\ \end{align}

Last updated date: 02nd Aug 2024
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Hint: For a) we know that the face value is the digit multiplied by its place value and 9 is placed in tens place. b) Now the given number is 673. After interchanging hundreds and tens digit the number will become 763. We will find the difference by subtracting larger numbers from smaller numbers. c) In the given sequence 5, 8, 11, 14, 17….. We can see that each number is increased by 3 to obtain the next number. d) Even numbers are the numbers which have 2, 4, 6, 8, and 0 in its units place. Hence, we will list such numbers and count them.

Now consider question a)
Now first consider the number 691.
Here we know that 9 is in tens place. Hence its place value is 90
Now the face value is 9. Hence the sum of face value and place value is 9 + 90 = 99.
Now consider question b)
We know that Arun interchanges tens and hundreds of digits of the number 673.
Now here tens digit is 7 and hundreds digit is 6.
Hence after interchanging tens digit is 6 and hundreds digit is 7.
Hence the number obtained is 763.
Now let us take the difference of obtained number and original number
Hence we get 763 – 673 = 90
Hence the number is increased by 90.
Now consider question c)
The given sequence is 5, 8, 11, 14, 17….
Now in this sequence let us check the difference of consecutive terms
8 – 5 = 3
11 – 8 = 3
14 – 11 = 3
17 – 14 = 2
Hence we can say that the common difference is 3.
Now let x be the next number
Hence we get x – 17 = 3.
Which means x = 17 + 3 = 20
Hence the next number in the sequence is 20.
Now consider our last option d)
Even numbers are numbers which are divisible by 2.
Now let us first list all the numbers between 40 to 60.
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59.
Now if the unit's place of number is divisible by 2 then the number is divisible by 2.
Hence the numbers with units place 0, 2, 4, 6, 8 are divisible by 2.
Hence in between 40 to 60, the numbers which are divisible by 2 are.
42, 44, 46, 48, 50, 52, 54, 56, 58.
Hence there are total 9 even numbers between 40 and 60

Note: Now note that while solving question d) since we are finding the numbers between 40 and 60, we will not consider these two numbers in our list. Also for option a) always note that face value is the digit itself and to find place value first find where the digit is placed and multiply by face value.