Question

if six times the larger of two numbers is divided by the smaller one we get 8 as quotient and 6 as remainder also if 9 times the smaller number is divided by the larger one we get 6 as quotient and 9 as remainder find the numbers

Answer 1

Given: If six times the larger of two numbers is divided by the smaller one we get 8 as quotient and 6 as remainder also if 9 times the smaller number is divided by the larger one we get 6 as quotient and 9 as remainder.

To find: The numbers?

Solution:

• Now according to the condition the two numbers are required.

• So let the larger number be x.

• Let the smaller number be y.

• Now question says :

                 six times the larger of two numbers is divided by the smaller one we get 8 as quotient and 6 as remainder

                 6x = 8y + 6

                 6x - 8y = 6        .......(i)

                 Also if 9 times the smaller number is divided by the larger one we get 6 as quotient and 9 as remainder

                 9y = 6x + 9

                 6x - 9y = -9      .....(ii)

• Now solving both the equations, we get:

                         6x - 8y = 6

                     -   6x + 9y = 9

                                y = 15

• Putting y = 15 in (i), we get:

                 6x - 8(15) = 6

                 6x = 6 + 120

                 6x = 126

                 x = 21

                 x = 21 and y = 15

Answer:

            So, the required numbers are 21 and 15.

Answer 2

Answer:

Larger number:21

Smaller number:15

Step-by-step explanation:

Let the larger number be'x' and the smaller number be 'y'.

Six times larger number by smaller

number:

6x/y=8+remainder

6x=8y+remainder

6x=8y+6

6x-8y-6

Nine times smaller number by larger

number:

9y/x=6+remainder

9y=6x+9

-6x+9y-9

Add and

6x-8y=6

-6x+9y=9

y=15

Substitute y=15 in

-6x+9(15)=9

-6x+135=9

6x=135-9

6x=126

X=126/6

x=21..