Find the least number which when divided by 35,45 and 55 leaves the reminder 18,28 and 38

Find the least number which when divided by 35,45 and 55 leaves the reminder 18,28 and 38 respectively
(a) 2981
(b) 2670
(c) 3120
(d) 3448

Anurag Mishra Professor Asked on 29th February 2016 in Maths.
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    Answer: (d) 3448 

    Explanation:-
    The factors of 35 = 5 x 7
    The factors of 45 = 3 x 3 x 5
    The factors of 55 = 5 x 11

    Then, the L. C. M. of 35, 45 and 55 = 3 x 3 x 5 x 7 x 11
    = 3465

    The difference between divisor and remainder = 35 – 18 = 17, 45 – 28 = 17 & 55 – 38 = 17.

    Then, required number = 3465 – 17
    = 3448

    Hence, the correct answer is option (d) 3448.

    Anurag Mishra Professor Answered on 4th March 2016.
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