26% of A = 832. What is the value of 31% of A?

$$\frac{26}{100}\times A$$ = 832 we get  A= $$832\times\left(\frac{100}{26}\right)$$ = 3200

now 31% of A = $$\frac{31}{100}\times 3200$$ = 992

alternatively,

it can be done using digital sum without out simplification

How to take out digital sum ? The digital sum of a number is the sum of the digits of the number till we get a single digit. For example let us take a number 

567892, the digital sum of this number is 5+6+7+8+9+2 = 37 now 3+7 =10 again 1+0 =1 so the digital sum of 567892 is 1

In the given question 

A= $$832\times\left(\frac{100}{26}\right)$$

31% of A =$$\frac{31}{100}\times 832 \times\frac{100}{26}$$ = $$\frac{31}{26}\times 832$$

calculating digital sum of 31 is 3+1 = 4 , 26 is 2+6 = 8 and 832 is 8+3+2 = 13 again adding the digits we get(1+3) = 4 

using the digital sum of the numbers as shown below

31% of A =$$\frac{31}{100}\times 832 \times\frac{100}{26}$$ = $$\frac{31}{26}\times 832$$ we get $$\frac{4}{8}\times 4$$ = 2

now to check for the answers we have to take out digital sum for all the options

option A 968 digital sum is 9+6+8 = 23 again 2+3 = 5 ( doesn't match the answer we got so incorrect)

option C 876 digital sum is 8+7+6 = 21 again 2+1 = 3 ( incorrect)

option D 854 digital sum is 8+5+4 = 17 again 1+7 = 8 (incorrect)

option B 992 digital sum is 9+9+2 = 20 again 2+ 0 =2 ( it matches the answer we got so it is correct)

This technique of digital sum might not always work for example when you have 2 or 3 options with same digital sum