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Playing with Numbers — Maths STD 8 — Question

Maharashtra BoardEnglish MediumSTD 8MathsPlaying with Numbers4 Marks
Question
Replace A, B, C by suitable numerals.
$ \ \ \ \ \ \ \ \ \ \ \ \text{A B}\\\underline{ \ \ \ \ \ \ \times\text{B A}}\\\underline{\text{(B+1)}\text{C B}}$
✓

Answer

A × B = B
⇒ A = 1
$\ \ \ \ \ \ \ \ 1\ \ \ \ \ \ \ \ \text{B}\\\underline{\times\ \ \ \ \ \text{B}\ \ \ \ \ \ \ 1\ \ \ \ }\\\underline{ \ \ \ \ \ \ \ \ 1\ \ \ \ \ \ \ \ \text{B}\\ \ \text{B }\ \ \ \text{B}^{2}\ \ \ \ \ \ \times\ }\\\text{B}\ \ (1+\text{B}^{2}) \ \text{B}$
In the equation:
First digit = B + 1
Thus 1 will be carried from $1+B^2$ and becomes $\left.(B+1)\left(B^2-9\right) B\right]$ $\$$ therefore\$ C = $B ^2-1$
Now all $b , B +1$ and $B ^2-9$ are one digit number.
This condition is satisfied for $B =3$ or $B =4$.
For, $B <3, B-9$ will be negative.
For, $B >3, B^2-9$ will become digit number.
For $B =3, C =3^2-9=9-9=0$
For, $B=4, C=4^2-9=16-9=7$
$\$$ therefore $\$ A=1, B=4, C =7$

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