Question

sum of two no is 97 . if the greater no is divided by the smaller, the quotient is 7 and the remainder is 1. find the numbers.

Answer 1

Solution. Let the larger number be x and smaller number be y.As per the first given condition,x + y = 97 ........eq. no. (1)As per the second condition,Dividend = Divisor × Quotient + Remainderx = y × 7 + 1∴  x = 7y + 1∴  x – 7y = 1 .......(2)Subtracting (2) from (1),x + y = 97x – 7y = 1(-)  (+)   (-)      8y = 98∴ y = 96/8∴ y = 12Substituting y = 12 in equation (1)∴ x + y = 97∴ x + 12 = 97∴ x = 97 – 12∴ x = 85
∴ The two numbers are 85 and 12.


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