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Exercise 4.2                                                                     PAGE: 4.8 
1. A magic square is an array of numbers having the same number of rows and columns and the sum of 
numbers in each row, column or diagonal being the same. Fill in the blank cells of the following magic 
squares: 
(i)  
 
(ii)  
 
Solution: 
 
(i) We know that  
Considering diagonal values 13 + 12 + 11 = 36 
So we get 
No. in the first cell of the first row = 36 – (8 + 13) = 15 
No. in the first cell of the second row = 36 – (15 + 11) = 10 
No. in the third cell of the second row = 36 – (10 + 12) = 14 
No. in the second cell of the third row = 36 – (8 + 12) = 16 
No. in the third cell of the third row = 36 – (11 + 16) = 9 
 
 
(ii) We know that 
Considering diagonal values 20 + 19 + 18 + 17 + 16 = 90 
So we get 
No. in the second cell of the first row = 90 – (22 + 6 + 13 + 20) = 29 
No. in the first cell of the second row = 90 – (22 + 9 + 15 + 16) = 28 
No. in the fifth cell of the second row = 90 – (28 + 10 + 12 + 19) = 21 
No. in the fifth cell of the third row = 90 – (9 + 11 + 18 + 25) = 27 
No. in the fifth cell of the fourth row = 90 – (15 + 17 + 24 + 26) = 8 
No. in the second cell of the fifth row = 90 – (29 + 10 + 11 + 17) = 23 
No. in the third cell of the fifth row = 90 – (6 + 12 + 18 + 24) = 30 
Page 2


 
 
 
 
 
 
Exercise 4.2                                                                     PAGE: 4.8 
1. A magic square is an array of numbers having the same number of rows and columns and the sum of 
numbers in each row, column or diagonal being the same. Fill in the blank cells of the following magic 
squares: 
(i)  
 
(ii)  
 
Solution: 
 
(i) We know that  
Considering diagonal values 13 + 12 + 11 = 36 
So we get 
No. in the first cell of the first row = 36 – (8 + 13) = 15 
No. in the first cell of the second row = 36 – (15 + 11) = 10 
No. in the third cell of the second row = 36 – (10 + 12) = 14 
No. in the second cell of the third row = 36 – (8 + 12) = 16 
No. in the third cell of the third row = 36 – (11 + 16) = 9 
 
 
(ii) We know that 
Considering diagonal values 20 + 19 + 18 + 17 + 16 = 90 
So we get 
No. in the second cell of the first row = 90 – (22 + 6 + 13 + 20) = 29 
No. in the first cell of the second row = 90 – (22 + 9 + 15 + 16) = 28 
No. in the fifth cell of the second row = 90 – (28 + 10 + 12 + 19) = 21 
No. in the fifth cell of the third row = 90 – (9 + 11 + 18 + 25) = 27 
No. in the fifth cell of the fourth row = 90 – (15 + 17 + 24 + 26) = 8 
No. in the second cell of the fifth row = 90 – (29 + 10 + 11 + 17) = 23 
No. in the third cell of the fifth row = 90 – (6 + 12 + 18 + 24) = 30 
 
 
 
 
 
 
 
 
2. Perform the following subtractions and check your results by performing corresponding additions: 
(i) 57839 – 2983 
(ii) 92507 – 10879 
(iii) 400000 – 98798 
(iv) 5050501 – 969696 
(v) 200000 – 97531 
(vi) 3030301 – 868686 
Solution: 
 
(i) 57839 – 2983 
We know that  
57839 – 2983 = 54856 
By addition 
54856 + 2983 = 57839 
 
(ii) 92507 – 10879 
We know that 
92507 – 10879 = 81628 
By addition 
81628 + 10879 = 92507 
 
(iii) 400000 – 98798 
We know that 
400000 – 98798 = 301202 
By addition 
301202 + 98798 = 400000 
 
(iv) 5050501 – 969696 
We know that 
5050501 – 969696 = 4080805 
By addition 
4080805 + 969696 = 5050501 
 
(v) 200000 – 97531 
We know that 
200000 – 97531 = 102469 
By addition 
102469 + 97531 = 200000 
 
(vi) 3030301 – 868686 
We know that 
Page 3


 
 
 
 
 
 
Exercise 4.2                                                                     PAGE: 4.8 
1. A magic square is an array of numbers having the same number of rows and columns and the sum of 
numbers in each row, column or diagonal being the same. Fill in the blank cells of the following magic 
squares: 
(i)  
 
(ii)  
 
Solution: 
 
(i) We know that  
Considering diagonal values 13 + 12 + 11 = 36 
So we get 
No. in the first cell of the first row = 36 – (8 + 13) = 15 
No. in the first cell of the second row = 36 – (15 + 11) = 10 
No. in the third cell of the second row = 36 – (10 + 12) = 14 
No. in the second cell of the third row = 36 – (8 + 12) = 16 
No. in the third cell of the third row = 36 – (11 + 16) = 9 
 
 
(ii) We know that 
Considering diagonal values 20 + 19 + 18 + 17 + 16 = 90 
So we get 
No. in the second cell of the first row = 90 – (22 + 6 + 13 + 20) = 29 
No. in the first cell of the second row = 90 – (22 + 9 + 15 + 16) = 28 
No. in the fifth cell of the second row = 90 – (28 + 10 + 12 + 19) = 21 
No. in the fifth cell of the third row = 90 – (9 + 11 + 18 + 25) = 27 
No. in the fifth cell of the fourth row = 90 – (15 + 17 + 24 + 26) = 8 
No. in the second cell of the fifth row = 90 – (29 + 10 + 11 + 17) = 23 
No. in the third cell of the fifth row = 90 – (6 + 12 + 18 + 24) = 30 
 
 
 
 
 
 
 
 
2. Perform the following subtractions and check your results by performing corresponding additions: 
(i) 57839 – 2983 
(ii) 92507 – 10879 
(iii) 400000 – 98798 
(iv) 5050501 – 969696 
(v) 200000 – 97531 
(vi) 3030301 – 868686 
Solution: 
 
(i) 57839 – 2983 
We know that  
57839 – 2983 = 54856 
By addition 
54856 + 2983 = 57839 
 
(ii) 92507 – 10879 
We know that 
92507 – 10879 = 81628 
By addition 
81628 + 10879 = 92507 
 
(iii) 400000 – 98798 
We know that 
400000 – 98798 = 301202 
By addition 
301202 + 98798 = 400000 
 
(iv) 5050501 – 969696 
We know that 
5050501 – 969696 = 4080805 
By addition 
4080805 + 969696 = 5050501 
 
(v) 200000 – 97531 
We know that 
200000 – 97531 = 102469 
By addition 
102469 + 97531 = 200000 
 
(vi) 3030301 – 868686 
We know that 
 
 
 
 
 
 
3030301 – 868686 = 2161615 
By addition 
2161615 + 868686 = 3030301 
 
3. Replace each * by the correct digit in each of the following: 
(i)  
 
(ii)  
 
(iii)  
 
(iv)  
 
(v)  
 
(vi)  
 
Solution: 
 
(i) We know that in the units digit  
6 - * = 7 where the value of * is 9 as 1 gets carried from 7 at tens place to 6 at units place  
6 at the units place becomes 16 so 16 – 9 = 7 
When 7 is reduced by 1 it gives 6 so 6 – 3 = 3 
We know that 
8 - * = 6 so we get * value as 2 
 
 
(ii) We know that in the units digit 
Page 4


 
 
 
 
 
 
Exercise 4.2                                                                     PAGE: 4.8 
1. A magic square is an array of numbers having the same number of rows and columns and the sum of 
numbers in each row, column or diagonal being the same. Fill in the blank cells of the following magic 
squares: 
(i)  
 
(ii)  
 
Solution: 
 
(i) We know that  
Considering diagonal values 13 + 12 + 11 = 36 
So we get 
No. in the first cell of the first row = 36 – (8 + 13) = 15 
No. in the first cell of the second row = 36 – (15 + 11) = 10 
No. in the third cell of the second row = 36 – (10 + 12) = 14 
No. in the second cell of the third row = 36 – (8 + 12) = 16 
No. in the third cell of the third row = 36 – (11 + 16) = 9 
 
 
(ii) We know that 
Considering diagonal values 20 + 19 + 18 + 17 + 16 = 90 
So we get 
No. in the second cell of the first row = 90 – (22 + 6 + 13 + 20) = 29 
No. in the first cell of the second row = 90 – (22 + 9 + 15 + 16) = 28 
No. in the fifth cell of the second row = 90 – (28 + 10 + 12 + 19) = 21 
No. in the fifth cell of the third row = 90 – (9 + 11 + 18 + 25) = 27 
No. in the fifth cell of the fourth row = 90 – (15 + 17 + 24 + 26) = 8 
No. in the second cell of the fifth row = 90 – (29 + 10 + 11 + 17) = 23 
No. in the third cell of the fifth row = 90 – (6 + 12 + 18 + 24) = 30 
 
 
 
 
 
 
 
 
2. Perform the following subtractions and check your results by performing corresponding additions: 
(i) 57839 – 2983 
(ii) 92507 – 10879 
(iii) 400000 – 98798 
(iv) 5050501 – 969696 
(v) 200000 – 97531 
(vi) 3030301 – 868686 
Solution: 
 
(i) 57839 – 2983 
We know that  
57839 – 2983 = 54856 
By addition 
54856 + 2983 = 57839 
 
(ii) 92507 – 10879 
We know that 
92507 – 10879 = 81628 
By addition 
81628 + 10879 = 92507 
 
(iii) 400000 – 98798 
We know that 
400000 – 98798 = 301202 
By addition 
301202 + 98798 = 400000 
 
(iv) 5050501 – 969696 
We know that 
5050501 – 969696 = 4080805 
By addition 
4080805 + 969696 = 5050501 
 
(v) 200000 – 97531 
We know that 
200000 – 97531 = 102469 
By addition 
102469 + 97531 = 200000 
 
(vi) 3030301 – 868686 
We know that 
 
 
 
 
 
 
3030301 – 868686 = 2161615 
By addition 
2161615 + 868686 = 3030301 
 
3. Replace each * by the correct digit in each of the following: 
(i)  
 
(ii)  
 
(iii)  
 
(iv)  
 
(v)  
 
(vi)  
 
Solution: 
 
(i) We know that in the units digit  
6 - * = 7 where the value of * is 9 as 1 gets carried from 7 at tens place to 6 at units place  
6 at the units place becomes 16 so 16 – 9 = 7 
When 7 is reduced by 1 it gives 6 so 6 – 3 = 3 
We know that 
8 - * = 6 so we get * value as 2 
 
 
(ii) We know that in the units digit 
 
 
 
 
 
 
9 – 4 = 5 
Tens digit 8 – 3 = 5 
So the missing blank can be found by subtracting 3455 from 8989 
Difference between them = 3455 
So the answer is 
 
 
(iii) We know that in units digit  
17 – 8 = 9  
Tens digit = 9 – 7 = 2 
So we get 
Hundreds place 10 – 9 = 1 
Thousands place 9 – 8 = 1 
So the addend difference = 5061129 
Subtract 5061129 from 6000107 to get addend 
 
So the answer is 
 
 
(iv) We know that in units digit  
10 – 1 = 9 
Lakhs place 9 – 0 = 9 
So the addend difference = 970429 
Subtract 970429 from 1000000 to get the addend 
 
So the correct answer is 
 
 
(v) We know that in units digit  
13 – 7 = 6 
Tens digit 9 – 8 = 1 
Hundreds place 9 – 9 = 0 
Thousands place 10 – 6 = 4 
So the addend difference = 4844016 
Page 5


 
 
 
 
 
 
Exercise 4.2                                                                     PAGE: 4.8 
1. A magic square is an array of numbers having the same number of rows and columns and the sum of 
numbers in each row, column or diagonal being the same. Fill in the blank cells of the following magic 
squares: 
(i)  
 
(ii)  
 
Solution: 
 
(i) We know that  
Considering diagonal values 13 + 12 + 11 = 36 
So we get 
No. in the first cell of the first row = 36 – (8 + 13) = 15 
No. in the first cell of the second row = 36 – (15 + 11) = 10 
No. in the third cell of the second row = 36 – (10 + 12) = 14 
No. in the second cell of the third row = 36 – (8 + 12) = 16 
No. in the third cell of the third row = 36 – (11 + 16) = 9 
 
 
(ii) We know that 
Considering diagonal values 20 + 19 + 18 + 17 + 16 = 90 
So we get 
No. in the second cell of the first row = 90 – (22 + 6 + 13 + 20) = 29 
No. in the first cell of the second row = 90 – (22 + 9 + 15 + 16) = 28 
No. in the fifth cell of the second row = 90 – (28 + 10 + 12 + 19) = 21 
No. in the fifth cell of the third row = 90 – (9 + 11 + 18 + 25) = 27 
No. in the fifth cell of the fourth row = 90 – (15 + 17 + 24 + 26) = 8 
No. in the second cell of the fifth row = 90 – (29 + 10 + 11 + 17) = 23 
No. in the third cell of the fifth row = 90 – (6 + 12 + 18 + 24) = 30 
 
 
 
 
 
 
 
 
2. Perform the following subtractions and check your results by performing corresponding additions: 
(i) 57839 – 2983 
(ii) 92507 – 10879 
(iii) 400000 – 98798 
(iv) 5050501 – 969696 
(v) 200000 – 97531 
(vi) 3030301 – 868686 
Solution: 
 
(i) 57839 – 2983 
We know that  
57839 – 2983 = 54856 
By addition 
54856 + 2983 = 57839 
 
(ii) 92507 – 10879 
We know that 
92507 – 10879 = 81628 
By addition 
81628 + 10879 = 92507 
 
(iii) 400000 – 98798 
We know that 
400000 – 98798 = 301202 
By addition 
301202 + 98798 = 400000 
 
(iv) 5050501 – 969696 
We know that 
5050501 – 969696 = 4080805 
By addition 
4080805 + 969696 = 5050501 
 
(v) 200000 – 97531 
We know that 
200000 – 97531 = 102469 
By addition 
102469 + 97531 = 200000 
 
(vi) 3030301 – 868686 
We know that 
 
 
 
 
 
 
3030301 – 868686 = 2161615 
By addition 
2161615 + 868686 = 3030301 
 
3. Replace each * by the correct digit in each of the following: 
(i)  
 
(ii)  
 
(iii)  
 
(iv)  
 
(v)  
 
(vi)  
 
Solution: 
 
(i) We know that in the units digit  
6 - * = 7 where the value of * is 9 as 1 gets carried from 7 at tens place to 6 at units place  
6 at the units place becomes 16 so 16 – 9 = 7 
When 7 is reduced by 1 it gives 6 so 6 – 3 = 3 
We know that 
8 - * = 6 so we get * value as 2 
 
 
(ii) We know that in the units digit 
 
 
 
 
 
 
9 – 4 = 5 
Tens digit 8 – 3 = 5 
So the missing blank can be found by subtracting 3455 from 8989 
Difference between them = 3455 
So the answer is 
 
 
(iii) We know that in units digit  
17 – 8 = 9  
Tens digit = 9 – 7 = 2 
So we get 
Hundreds place 10 – 9 = 1 
Thousands place 9 – 8 = 1 
So the addend difference = 5061129 
Subtract 5061129 from 6000107 to get addend 
 
So the answer is 
 
 
(iv) We know that in units digit  
10 – 1 = 9 
Lakhs place 9 – 0 = 9 
So the addend difference = 970429 
Subtract 970429 from 1000000 to get the addend 
 
So the correct answer is 
 
 
(v) We know that in units digit  
13 – 7 = 6 
Tens digit 9 – 8 = 1 
Hundreds place 9 – 9 = 0 
Thousands place 10 – 6 = 4 
So the addend difference = 4844016 
 
 
 
 
 
 
Subtract 4844016 from 5001003 to get the addend 
 
So the answer is  
 
 
(vi) We know that units digit  
11 – 9 = 2 
So the addend difference = 54322 
Subtract 54322 from 111111 to get the addend 
 
So the answer is 
 
 
4. What is the difference between the largest number of five digits and the smallest number of six digits? 
Solution: 
 
99999 is the largest number of five digits 
100000 is the largest number of six digits 
Difference = 100000 – 99999 = 1 
 
Therefore, 1 is the difference between the largest number of five digits and smallest number of six digits. 
 
5. Find the difference between the largest number of 4 digits and the smallest number of 7 digits. 
Solution: 
 
9999 is the largest number of 4 digits 
1000000 is the smallest number of 6 digits 
Difference = 1000000 – 9999 = 990001 
 
Therefore, 990001 is the difference between the largest number of 4 digits and the smallest number of 7 digits. 
 
6. Rohit deposited Rs 125000 in his savings bank account. Later he withdrew Rs 35425 from it. How much 
money was left in his account? 
Solution: 
 
Money deposited in savings bank account = Rs 125000 
Money withdrawn = Rs 35425

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