Question

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

Answer 1

Let one of the number is x and another is y where x > y.

A/Q,

Sum of numbers = 97

⇒ x + y = 97

⇒ x = 97 - y   ------ ( 1 )

Now,

When x is divided by y then quotient is 7 and remainder is 1 .

⇒ x = 7 y + 1  ------ ( 2 )

From ( 1 ) and ( 2 ) we get ,

⇒ 97 - y = 7 y + 1

⇒ 97 - 1 = 7 y + y

⇒ 96 = 8 y

⇒ y = 96 ÷ 8

∴ y = 12.

By substituting the value of y in ( 1 ),

⇒ x = 97 - y

⇒ x = 97 - 12

∴ x = 85.

Verification : Sum of numbers = 97

               ⇒ 85 + 12 = 97

                ⇒ 97 = 97.

Again,

 ⇒ x = 7 y + 1

 ⇒ 85 = 7 x 12 + 1

 ⇒ 85 = 84 + 1

 ⇒ 85 = 85.

So , greater number = 85 and lesser number = 12.

Answer 2

Answer:

Let the greater number be x

Let the smaller number be y

According to first condition

x+y=97

x=97-y...(1)

According to second condition

x=7y+1 ....(2)

from (1) and (2)

97- y=7y+1

97-1=7y+y

96=8y

y=12

substitute y=12 in equation (1)

x=97-y

x=97-13

x=85

Therefore the greater number is 85 and smaller number is 12