Question

Find the Digits A and B

explain in brief about the answer with the points.

Refer the attachment:-​

Answer 1

$\huge\underline\red{Solution:-}$

$\mathsf{\red{This\:is\:numbers \:in general \:form }}$

This has two letters A and B whose value are to be found.

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Since, the ones digit of 3×A is A, it must be that A=0 or A =5.

Now look at B, If B=1,

Then BA×B3 would at most be equal to 19×19;

That is,it would at most be equal of 361,

But the product here is 57A, which is more than 500,So we cannot have B=1.

If B = 3, then BA× B3 would be more than 30 x 30; that is more than 900.

But 57 A is less than 600. So, B can not be equal to 3.

Putting these two facts together, we see that B = 2 only. So the multiplication is either

$20 x 23, \:or\: 25 x 23$

The first possibility fails, since 20 x 23 = 460.

But the, second one works out correctly one works out correctly, Hence 25×23=575.

Steps:-

$3×A=A$

$A=0 or A =5$

$B=1$

$BA×B3$

$19×19$

$B = 3, then BA× B3$

30 x 30; that is more than 900

57 A is less than 600

$20 x 23, \:or\: 25 x 23$

20 x 23 = 460

25×23=575

So, Hence therefore the Answer= $\huge\boxed{A=5,B=2}$