Need help in this percentage problem ?

I'm going to make up some variables with one, two, or 3-letter names

instead of the usual one-letter names, to keep track better.

So let

AJR = the percentage of people who like all three.

AJ = the percentage of people who like Ajay and John but not Ranbir.

AR = the percentage of people who like Ajay and Ranbir but not John.

JR = the percentage of people who like John and Ranbir but not Ajay.

A = the percentage of people who like only Ajay.

J = the percentage of people who like only John.

R = the percentage of people who like only Ranbir.

Now we can write equations for the given information:

{1} AJR + AR + JR + R = 41

{2} AJR + AJ + AR + A = 35

{3} AJR + AJ + JR + J = 60

{4} AJ + AR + JR = 27

{5} AJR + AJ + AR + JR + A + J + R = 97

{6} AJR + JR = 16

{7} AJR + AJ = 14

That's the given information. Now we need to solve for A.

{8} 3(AJR) + 2(AJ + AR + JR) + A + J + R = 136 [adding {1}, {2}, and {3}]

{9} 3(AJR) + AJ + AR + JR + A + J + R = 109 [subtracting {4} from {8}]

{10} 2(AJR) = 12 [subtracting {5} from {9}]

{11} AJR = 6 [dividing each side of {10} by 2]

{12} JR = 10 [subtracting {11} from {6}]

{13} AJ = 8 [subtracting {11} from {7}]

{14} AR = 9 [subtracting BOTH {12} and {13} from {4}]

{15} 6 + 8 + 9 + A = 35 [substituting for variables in {2}, using {11}, {13}, and {14}]

{16} A = 12 [solving {15} for A]