Question

If the sum of two numbers is divided by 3, the quotient is 4 and the remainder is 1. If the

difference of these two numbers is divided by 2, the quotient is 2 and the remainder is 1. Find

the two numbers.

Answer 1

The two numbers are 9 and 4.

• Let the two numbers be x and y.

• Now, the sum of x and y is equal to (x + y).

Given,

(x + y) / 3 leaves 4 as the quotient, and 1 as the remainder.

Here, dividend = (x + y)  [Dividend is the number which is divided ],

and divisor = 3  [ Divisor is the number by which dividend is divided ]

• The formula for a dividend is given as : Dividend = (Divisor × Quotient) + Remainder

• Therefore,

(x + y) = (3 × 4) + 1

=> x + y = 12 + 1

=> x + y = 13   -(i)

• Difference between x and y = x - y

Given,

(x - y) / 2 leaves 2 as the quotient, and 1 as the remainder.

Here, dividend = (x - y),

and divisor = 2

•  Using the formula, Dividend = (Divisor × Quotient) + Remainder,  we get,

(x - y) = (2 × 2) + 1

=> x - y = 4 + 1

=> x - y = 5  -(ii)

• Now, adding equations (i) and (ii), we get,

(x + y) + (x - y) = 13 + 5

=> x + y + x - y = 18

=> x + x + y - y = 18

=> 2x + 0 = 18

=> 2x = 18

=> x = 18 / 2

=> x = 9

The value of y can be calculated by putting the value of x in either equation (i) or equation (ii).

Therefore, putting  x = 9 in equation (ii), we get,

9 - y = 5

=> - y = 5 - 9

=> - y = - 4

=> y = 4

•∴  The numbers are 9 and 4.