## In a certain number is divided by the sum of its two digits, the quotient is 6 and remainder is 3. If the digits are interchanged and the r

Question

In a certain number is divided by the sum of its two digits, the quotient is 6 and remainder is 3. If the digits are interchanged and the resulting number is divided by the sum of its digits, then the quotient is 4 and the remainder is 9. Find the number​

in progress 0
3 weeks 2021-09-04T17:44:20+00:00 2 Answers 0 views 0

• The Number [According to question] .

## ☞ GIVEN:–

• In a certain number is divided by the sum of its two digits, the quotient is 6 and reminder is 3 .
• If the digits are interchanged and the resulting number is divided by the sum of its digits, then the quotient is 4 and reminder is 9 .

## ☞CALCULATION:–

(╬) Suppose the original Numbers,

• unit digit be x
• tens digit be y
• The Original Number = (10y + x)

(╬) According to question,

• (10y + x) is divided by (x + y) and we get 6 as a quotient and 3 as a reminder .
1. Dividend = (10y + x)
2. Divisor = (x + y)
3. Quotient = 6
4. Reminder = 3

———(1)

Again,

• If the digits are interchanged, we get (10x + y) as a number and (10x + y) is divided by (x + y) resulting 4 as a Quotient and 9 as a reminder .
1. Dividend = (10x + y)
2. Divisor = (x + y)
3. Quotient = 4
4. Reminder = 9

———(2)

Now, we solve the Equations (1) and (2) ,

• see the attachment picture for solvation of Equations (1) and (2)

we get,

• x = 5 and y = 7 .

Therefore, The original Number is ,

• Here we use formula of checking division to setting up the equation as per the given Question]

• A certain number is divided by the sum of its two digits, the quotient is 6 and remainder is 3.]

=>Dividend=Divisor×Quotient+Remainder:

• If the digits are interchanged and the resulting number is divided by the sum of its digits, then the quotient is 4 and the remainder is 9.]

• Here diving by 3 on both sides]

• Now in eq (ii) multiplying by 4 than subtracting from from equation (i) here]

• By solving we get, here]

• Putting the value of y=5 in eq (ii) here]

Hence,

• The certain number=10x+y
• The certain number=10×7+5
• The certain number=70+5
• The certain number=75