24p leaves remainder 1 if it is divided by 3 and leaves remainder 2 if it is divided by 5. Find the value of p.
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Answer:
As 24P is a number, then P must be a unit digit.
(i) Since, on dividing by 3 remainder is 1.
This implies that P can be 4,7 as
3
240+P
=80+
3
P
and
3
P
gives 1 as remainder. Hence, P=4 or 7
(ii) Now, on dividing by 5 remainder is 2.
This implies that P must be 7 as
5
240+P
=48+
5
P
and
5
P
gives 2 as remainder. Hence, P=7
Both Conditions (i), (ii) implies P=7.
Therefore, answer is P→7
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