RBSE Class 10 Maths Chapter 1 Vedic Mathematics Ex 1.1

Question 1. Solution. Steps:

1. 73 + 70 = 70 + 30 + 43 = 100 + 43 = 143

Hence (RBSESolutions.com) mark an Ekadhika dot on 4 before 70.

2. Rest 42 + 54 + 89 = 89 + 11 + 43 + 43 = 100 + 86 = 186

Hence mark on Ekadhika dot on 2 before 89.

3. Rest 86 + 75 = 86 + 41 + 61 = 100 + 6 = 161

Hence mark on Ekadhika dot on 0 before 75.

4. Rest 61 + 01 = 62

5. The remaining addition process will be completed accordingly.

Question 2. Solution. Steps :

1. 36 + 28 = 36 + 4 + 24 = 40 + 24 = 64 + 99 = 99 + 1 + 63 = 100 + 63 = 163

Hence, mark (RBSESolutions.com) a dot on 9 before 99.

2. Rest 63 + 21 = 84

Hence, write 84 at answer’s place.

3. The remaining addition process will be completed accordingly.

Subtract by Vedic Method

Question 3. Solution. Steps:

∴ 7 cannot be subtracted from 6.

So add completed digit 3 of 7 to 6 and write 9 in total along with mark an Ekadhik on previous digit 6 of 7.

Thus, complete the subtraction process.

Question 4. Solution. ∴ 12 hr 27 m 28 sec.

Steps:

1. Measurement (RBSESolutions.com) unit in ‘time’ column-wise base is different.
2. In column of minute and second there will be two base.

• (a) Base in unit column of both = 10
• (b) Base in time column of both = 6
3. Base in column of hour =10
4. The base of getting complement digits in the tens columns of minute and second = 6 and in remaining base = 10

Remark: General base considered in decimal.

Multiply

Question 5.

31 × 31 Solution. Question 6.

103 × 197 (By Ekadhikena Poorvena Sutra)

Solution.

103 × 197 = 1 × 2/03 × 97 = 2/0291 = 20291

Question 7.

54 × 56 (By Sutra Nikilam)

Solution.

54 × 56 = 54 + 4 + 56 + 6 = 5(54 + 6)/4 × 6 = 5 × 60/24

[In R.H.S. two digits (RBSESolutions.com) and sutra is effective]

= 300/24 = 3024

Question 8.

108 × 112 (By Sutra Nikhilam)

Solution.

108 × 112 = 108 + 08 × 112 + 12

= 1(108 + 12)/08 × 12 = 1 × 120/90 = 12096

Question 9.

137 × 9999 (By sutra Ekanyunena Poorvena)

Solution.

137 × 9999

L.H.S = 0137 – 1 = 0136

R.H.S. = 9999 – 0136 = 9863

137 × 9999 = 0137 – 1/9999 – 0136 = 1369863

Question 10.

46 × 99 (By sutra Ekanyunena Poorvena)

Solution.

46 × 99

L.H.S. = 46 – 1 = 45

R.H.S. = 99 – 45 = 54

46 × 99 = 46 – 1/99 – 45 = 4554

Question 11.

362 × 143 (By Sutra Urdhva triyak)

Solution. Question 12.

2413 × 3124 (By Sutra Urdhva Triyagbhayam)

Solution.

7 group (RBSESolutions.com) formed Divide [Question 13 to 20]

Question 13.

111034 ÷ 889 (By Sutra Nikhilam)

Solution. Divisor = 889

Revised divisor = base – divisor = 1000 – 889 = 111

Quotient = 124

Remainder = 798

Question 14.

3994 ÷ 97 (By Sutra Nikhilam)

Solution. base = 100

Revised divisor = 100 – 97 = 03

Quotient = 41

Remainder = 17

Question 15.

2112 ÷ 97 (By Sutra Pravartya)

Solution.

This question is (RBSESolutions.com) solved by Nikhilam method not suitable for pravartya sutra. Quotient = 21

Revised divisor = 75

Question 16.

13385 ÷ 131 (By Sutra Pravartya)

Solution. Now, Quotient = 102

Remainder = 23

Question 17.

592837 ÷ 119 (By Sutra Dhwajank)

Solution.  Question 18.

58764 ÷ 59 (By Sutra Dhwajank)

Solution. 1. Divisor = 59, Mukhyank = 5, Dhwajank = 9
2. In third column one digit of divident = 4
3. 58 ÷ 5 = 11, Quotient = 11, Remainder = 3.
4. Corrected dividend = 37 – 11 ÷ 9 = 37 – 99

Since corrected (RBSESolutions.com) dividend is negative so the second digit of quotient must be 9 instead of 11.

That is why the terms (ii) and (iv) are rejectable.

5. Again 58 ÷ 5, Quotient first digit = 9, Remainder = 13
6. New dividend = 137,

Corrected dividend = 137 – 9 × 9 = 56

7. 56 ÷ 5, Quotient second digit = 9, Remainder = 11
8. New dividend = 116,

Correctly divisor = 116 – 9 × 9 = 35

9. 35 ÷ 5, Quotient second digit = 6, Remainder = 5
10. New divisor = 54

Corrected divisor and final remainder = 54 – 6 × 9 = 54 – 54 = 0.

Thus quotient = 996, Remainder = 0.

Question 19.

92358 ÷ 151 (by dhwajank sutra)

Solution. Hint :

1. Divisor = 151, Mukhyank 15, Dhwajank = 1
2. In third (RBSESolutions.com) column one digit of dividend = 8
3. 92 ÷ 15, Quoient first digit = 6, Remainder = 2
4. New dividend = 23, corrected dividend = 23 – 6 x 1 = 17
5. 17 ÷ 15, Quotient second digit = 1, Remainder = 2
6. New dividend 25, correctly dividend = 25 – 1 × 1 =24
7. 24 ÷ 15, quotient third digit = 1, Remainder = 9
8. New dividend = 98.

Corrected dividend are final remainder = 98 – 1 × 1 = 97

Quotient = 611, Remainder = 97

Question 20.

12345 ÷ 91 (By Sutra Dhwanjank)

Solution. Hint:

1. Divisor = 91, Mukhaynak = 9, dhwajank = 1
2. In third part divided one digit = 5
3. 12 ÷ 9 = Quotient first digit = 1, Remainder = 3
4. New dividend = 33, (RBSESolutions.com) Corrected dividend = 33 – 1 × 1 = 32
5. 32 ÷ 9 quotient second digit = 3, Remainder = 5
6. New dividend = 54, corrected dividend = 54 – 3 × 1 = 51
7. 51 ÷ 9 quotient third digit = 5, Remainder = 6
8. New dividend = 65,

Corrected dividend or final remainder = 65 – 5 × 1 = 60

Quotient = 135, Remainder = 60