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 +
Remainder
x = y × 7 + 1
∴ x = 7y + 1
∴
x – 7y = 1 .......(2)
Subtracting (2) from (1),
x + y = 97
|
x – 7y = 1
|
(-) (+)
(-)
|
8y = 98
|
∴ y = 96/8
∴ y = 12
Substituting y = 12 in equation
(1)
∴ x + y = 97
∴ x + 12 = 97
∴ x = 97 – 12
∴ x = 85
∴ The two numbers are 85 and 12.