Question

(i) The sum of two numbers is 97. If the greater number is divided
by the smaller, the quotient is 7 and the remainder is 1. Find the number. ​

Answer 1

Answer:

greater number = 85 and lesser number = 12

Step-by-step explanation:

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