Each of the following four digit number is divisible by 9. Find the value of $x$
(i) $15 x 2$
(ii) $4 x 23$

(i) 1
(ii) 0 or 9

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(i) 1
(ii) 8 or 1

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(i)8
(ii) 9 or 0

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(i) 2
(ii) 3

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Solution

The correct option is A (i) 1
(ii) 0 or 9
$F o r t h e n u m b e r t o b e d i v i s i b l e b y 9, t h e s u m o f i t s d i g i t s s h o u l d b e a m u l t i p l e$
$o f 9, (i) 15 x 2 \to 1 + 5 + x + 2 = 9 n, ⟹ 8 + x = 9, ⟹ x = 1. (i i) 4 x 23 \to 4 + x + 2 + 3 = 9 n,$
Now, $x$ is a digit between 0 and 9. Hence, $n$ can take the values 1 or 2.
$⟹ 9 + x = 9 o r 18, ⟹ x = 0 o r 9.$

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