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Question 124

If the number obtained after subtracting x from 2035 leaves the same remainder 5 when it is divided by 9, 10 and 15, then the smallest possible x is

Solution

The given number in the question is $$=2035$$

Now, after subtracting x from the given number, new number will be $$2035-x$$

When we are dividing the $$2035-x$$ by $$9,10,15$$ it is leaving the remainder 5.

Now, the LCM of the number $$90$$

Now, when we are dividing the 2035 by 90, then it is leaving the remainder 55.

But as per the condition, the remainder should be 5. hence the required number $$=55-5=50$$

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