If c > a; show that cba – abc = 99(c – a). - Vidyadip

Question

If $c > a$; show that $cba – abc = 99(c – a).$

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Answer

Given : $ c > a$
To show : $cba – abc = 99(c – a)$
Proof:
$cba = 100c + 106 + a ……….(i)$
$($By using property $3)$
$abc = 100a + 106 + c ………(ii)$
$($By using property $3)$
Subtracting $(ii)$ from$ (i)$
$cba – abc= 100c+ 106 + a- 100a- 106-c$
$\Rightarrow cba – abc = 99c – 99a$
$\Rightarrow cba – abc = 99(c – a)$
Hence proved.

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