Question

Multiply 98, 97, 99 by Nikhilam formula of vedic maths.
A.941194
B.941094
C.941294
D.None of these

Answer 1

Hint: First of all, we subtract all the quantities that have to be multiplied with a base value example 10, 100, etc. depending on the number of digits in the given number. Then we represent the two quantities that are the given numbers and the difference between the number and base value on two different sides. And then solve it by the Nikhilam formula of Vedic maths.

Complete step-by-step answer:
We have to find the given numbers are all two-digit numbers so we take the base 100. We write the numbers on the left side and the difference between the given number and 100 on the $ 98 \times 97 \times 99 $ e right side. The difference between - 98 and 100 is -2, 97 and 100 is -3, 99 and 100 is -1, so we get –
 $
  98\,\,\,\,\,\,\,\, - 2 \\
  97\,\,\,\,\,\,\,\, - 3 \\
  99\,\,\,\,\,\,\,\, - 1 \;
  $
Now, the result is divided into three parts, in the right part we write the sum of all the terms given on the right side of the above representation that is the sum of $ - 2, - 3, - 1 $ . In the middle part, we write the sum of the product of two terms with each other that is the sum of $ ( - 2) \times ( - 3),\,( - 3) \times ( - 1),\,( - 2) \times ( - 1) $ and in the left part, we write the sum of the given number with all the terms of the right side except the one in front of it that is $ 98 + ( - 3) + ( - 1),\,97 + ( - 2) + ( - 1),\,99 + ( - 2) + ( - 3) $ , thus we get –
 $
  \underline
  98\,\,\,\,\,\,\,\,\,\,\,\, - 2 \\
  97\,\,\,\,\,\,\,\,\,\,\,\, - 3 \\
  99\,\,\,\,\,\,\,\,\,\,\,\, - 1 \\
    \\
  94 + ( - 3) + ( - 1)|[( - 2) \times ( - 3)] + [( - 3) \times ( - 1)] + [( - 2) \times ( - 1)]|( - 2)( - 3)( - 1) \\
  94|6 + 3 + 2| - 6 \\
  94|11| - 6 \;
  $
Now, we see that the term in the right part is negative so we subtract 1 from the middle part and tend to add it to the right part but instead of 1, we add the base quantity to the right part as shown,
 $
  94|11 - 1| - 6 + 100 \\
  94|10|94 \;
  $
Now, we merge the terms of the three parts and write them together as one term –
 $ \Rightarrow 941094 $
Thus, $ 98 \times 97 \times 99 $ is $ 941094 $ .
So, the correct answer is “Option B”.

Note: Students might misinterpret the formula of finding the product using Vedic math’s as division, the terms are just separated in columns, the symbol doesn’t represent division. Don’t get confused otherwise you may get the wrong answer. So, students must follow Vedic math’s method for solving such questions because it makes big calculations easier.