Multiple choice

A number when successively divided by 4, 5 and 6 gives reminder 2, 3 and 4. Find the remainder when the same number is divided by 60. एक संख्या को जब 4, 5 और 6 से लगातार से विभाजित किया जाता है, तो 2, 3 और 4 शेषफल प्राप्त होता है | उसी संख्या को जब 60 से विभाजित किया जाता है तो प्राप्त शेषफल ज्ञात कीजिये |

  1. 32

  2. 18

  3. 34

  4. 12
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C Correct answer
Explanation

Using successive division: N = 4a + 2, a = 5b + 3, b = 6c + 4. Working backwards: b = 6c + 4, a = 5(6c + 4) + 3 = 30c + 23, N = 4(30c + 23) + 2 = 120c + 94. When N is divided by 60, N = 60(2c) + 34, remainder = 34. Alternatively, use Chinese remainder theorem or direct substitution.

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