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If three times the larger of the two numbers isdivided by the smaller one, we get 4 as quotient and 3 as remainder. Also ifseven times the smaller number is divided by the larger one, we get 5 asquotient and 1 as remainder . Find the numbers. |
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Answer» Let the larger number be x and the smaller one by y . We know that dividend = ( divisor ` xx` quotient ) + remainder Using the above result and the given conditions, we have ` 3 x = 4y + 3 rArr 3 x - 4y = 3 " " `... (i) and ` 7y = 5 x + 1 rArr 5 x - 7y = - 1 " " `... (ii) Multiplying (i) by 5, (ii) by 3 and subtracting, we get ` y = 18` Putting `y = 18 ` in (i), we get ` 3 x - ( 4 xx 18) = 3 rArr 3x - 72 = 3 ` `rArr 3x = 75 rArr x = 25 ` Hence, the required numbers are 25 and 18. |
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