Question

sum of two numbers is 97if the larger is divided by the smaller, the quotient is 7 and the remainder is 1. find the numbers​

Answer 1

Question: Sum of two numbers is 97  if the larger is divided by the smaller, the quotient is 7 and the remainder is 1. find the numbers. Answer: Numbers are 85 and 12 Step-by-step explanation: given that, sum of two numbers is 97, let the numbers be x and y so, According to the question x + y = 97  .....(1) now, given that, if the larger is divided by the smaller, the quotient is 7 and the remainder is 1. let the larger number be x  means, dividend = x divisor = y  quotient = 7 remainder = 1 By the division theorem , dividend = divisor × quotient + remainder now, putting the values, x = y × 7 + 1 x = 7y + 1 x - 7y = 1  ....(2) now, equation (1) => x + y = 97 equation (2) => x - 7y = 1 subtracting equation (2) from (1) x + y - (x - 7y) = 97 - 1 x + y - x + 7y = 96 8y = 96 y = 96/8 y = 12 putting the value of y on (1) x + y = 97 x + 12 = 97 x = 97 - 12 x = 85 so, Numbers are 85 and 12

Answer 2

☞ Sum of two number is 97.

Let one number be M

and

Another number be N.

=> M + N = 97

=> M = 97 - N __________(eq 1)

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☞ The larger is divided by the smaller, then the quotient is 7 and remainder is 1.

Let larger number be M

and

Smaller number by N.

• Dividend = Divisor × Quotient + Remainder

Here..

Dividend = M

Quotient = 7N

Remainder = 1

• A.T.Q.

=> M = 7N + 1

=> 97 - N = 7N + 1 [From (eq 1)]

=> 97 - 1 = 7N + N

=> 96 = 8N

=> 8N = 96

=> N = 12

• Put value of N in (eq 1)

=> M = 97 - (12)

=> M = 85

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Numbers are : 85 and 12

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