Find the least number which when divided by 35 leaves a remainder 25, when divided by 45 leaves a remainder 35 and when divided by 55 leaves a remainder 45.

3465

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4575

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3455

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3670

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Solution

The correct option is C $3455$
Since $35 - 25 = 10, 45 - 35 = 10, 55 - 45 = 10$
i.e. the difference between any divisor and the
corresponding remainder is the same the
required number will be obtained by subtracting
10 from the LCM of $35, 45 a n d 55$
$∴$ Required number
$= L C M (35, 45, 55) - 10 = 3465 - 10 = 3455$

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Find the least number which when divided by 35 leaves a remainder 25, when divided by 45 leaves a remainder 35 and when divided by 55 leaves a remainder 45.

The correct option is C 3455Since 35−25=10,45−35=10,55−45=10i.e. the difference between any divisor and thecorresponding remainder is the same therequired number will be obtained by subtracting10 from the LCM of 35,45 and 55∴ Required number =LCM(35,45,55)−10=3465−10=3455