Question

find value of English alphabet AB×B=96​

Answer 1

Answer:

From the question, it is given that the units place contains a 6. So, the product of B and B should give a number with 6 in units place. It is possible when B = 4 or 6.

When B = 4,

(10A + B) x (B) = 96

It becomes (10A + 4) x 4 = 96 40A + 16 = 96,

By simplifying the equation, it gives A = 2.

Similarly, when B = 6,

(10A + B)x(B) = 96

By simplifying, it becomes (10A + 6) x 6 = 96

60A + 36 = 96, gives A = 1.

Hence, A = 2 B = 4 or A = 1 B = 6 (Both are feasible solutions)

Answer 2

Proper Question

Two alphabet letters A and B represent the digits, find the value of A and B in $AB\times B=96$.

Answer

$A=2, B=4$ or $A=1, B=6$.

Solution

Since the last digit of the product ends with a 6, B can be 4 or 6.

Let's consider each case.

① $B=4$

$\implies \underline{A}\ \underline{4}\ \times \ \underline{4}\ = 96$

$\implies \underline{A}\ \underline{4}\ =\ 96\ \div \ 4$

$\implies \underline{A}\ \underline{4}\ =\ 24$

In this case, A is 2.

② $B=6$

$\implies \underline{A}\ \underline{6}\ \times \ \underline{6}\ = 96$

$\implies \underline{A}\ \underline{6}\ =\ 96\ \div \ 6$

$\implies \underline{A}\ \underline{6}\ =\ 16$

In this case, A is 1.

Conclusion

So, the pair of the alphabet will be $A=2, B=4$ or $A=1, B=6$.