Question

Multiply 54, 57 using Nikhilam formula (sub-base) of vedic mathematics.
(A) 3278
(B) 3768
(C) 3078
(D) None of these

Answer 1

Hint: In this question two numbers are given and we have to multiply them by using the Nikhilam formula of vedic mathematics. In this method of multiplication first we find the power of 10 as base. Now to select the power of 10 we look at the numbers and whichever power of 10 is closer to the number that is our base. Then we subtract these numbers with the power of 10 and find their deviations and by using the cross addition of the numbers we obtain the digits of our answer.

Complete step-by-step answer:
Given:
The given numbers for the multiplication are –
$54$ and $57$
Now applying the Nikhilam method of multiplication we have –
$
\Rightarrow {\rm{5 4}}\\
 \times {\rm{ 5 7}}
$
(1) Both the numbers given are closer to the power of 10 that is base 100.
(2) Now subtracting both the numbers from 100 we get the value of the deviation for both the numbers.
So,
$\Rightarrow 100 - 54 = 46$
And,
$\Rightarrow 100 - 57 = 43$
So, the number 54 is 46 less than 100 and the number 57 is 43 less than 100 respectively.
(3) Now by multiplying both the deviations including their signs we get,
$
\Rightarrow \left( { - 46} \right) \times \left( { - 43} \right) = 1978\\
 = \left( {19{\rm{carry}}} \right){\rm{ 78}}
$
Since the base is 100 that means we need to have only two digits out of the four digits in the number 1978. So, we carry forward two initial digits 19 and use only 78.
(4) Now by cross addition of the numbers with deviations, we get,
$\Rightarrow 54 - 43 = 11$
And,
$\Rightarrow 57 - 46 = 11$
(5) Now finally adding the carry forward value 19 to the 11 we get,
$\Rightarrow 19 + 11 = 30$
Combining the answers obtained from steps (3) and (5) we get,
$\Rightarrow 54 \times 57 = 3078$

So, the correct answer is “Option C”.

Note: It should be noted that the Nikhilam formula of multiplication is simple when the numbers that we have to multiply are closer to the power of 10, otherwise the value of deviation is large and the multiplication of large numbers is more complex.