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When a certain number \( N \) is divided by 38 , the remainder is 16. When the same number \( N \) is divided by 48 , the quotient is 77 with some remainder \( R \). Find the value of number \( N \).(1) 3702(2) 3712(3) 3602(4) 3612 |
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Answer» N = 38q + 16 ⇒N - 16 = 38q ... (1) Similarly, ⇒ N = (48 × 77) + r (r is the remainder) ⇒ N = 3696 + r ... (2) From (1) and (2) ⇒ N > 3696 and N - 16 = 38q ⇒ Min(N) = 3698 (N - 16 should be even) ⇒ N - 16 ≥ 3682 and N - 16 = 38q ⇒ N - 16 > 3682 and N - 16 = 38q (3682 is not divisible by 38) ⇒ N - 16 = 3686 ∴ N = 3702 Hence, option (1) is correct. |
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