Question

What will be the value of a and b a8+96=1ab?

Answer 1

Value of b is 4 and a can be any number from 1 to 9.

Given:

$a8+96=1ab,$

To find:

Value of a and b = ?

Solution:

a and b which are the digits in the equation.

a8 is nothing but a×10 + 8 , as a is in 10’s place of a8.

$1ab = 1\times100 + a\times10 + b\times1$, as 1 is in 100’s place, a is in 10’s place and b is in 1’s place.

$= 100 +10\times a + b$

So, right hand side $= 100 + 10\times a + b$

Left hand side $= 10\times a + 8 + 96 = 10\times a + 104$

So,$10\times a + 104 = 100 + 10\times a + b$

As both sides are equal,we can compare the like terms which are of a and b

$104 = 100 + b \\b = 104-100 = 4$

right hand side $= 100 + 10\times a + b = 100 + 10\times a +4 = 104 + 10\times a$

Let us check for the value of a using trial and error method:

If $a=1,$

then LHS $= 18 + 96 = 114$

RHS $= 114$

If $a = 2,$

then LHS $= 28 + 96 = 124$

RHS $= 124$

If $a =3 ,$

then LHS $= 38 + 96 = 13$

RHS $= 134$

So,if b=4 ,a can be any number from 1 to 9.