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# a two-digit number is 4 times the sum of its digits and twice the product of the digits. find the number.

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## A two digit number is 4 times the sum of its digits and twice the product of its digits.The number is

Click here👆to get an answer to your question ✍️ A two digit number is 4 times the sum of its digits and twice the product of its digits.The number is - - - - - -

Question

## A two digit number is 4 times the sum of its digits and twice the product of its digits.The number is ------

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Updated on : 2022-09-05

Solution Verified by Toppr

Correct option is A)

Let the digit in the ones place be x and tens place be y

Hence the two digit number =10y+x

Given that the two digit number =4 times sum of its digits

According to the question,

⇒  10y+x=4(x+y) ⇒  10y+x=4x+4y ⇒  3x−6y=0

⇒  x=2y                   ------- ( 1 )

It is also given that the two digit number =2 times product of its digits

⇒  10y+x=2xy

Divide by xy both the sides, we get

⇒ x 10 ​ + y 1 ​ =2

Put x=2y from (1), we get

⇒ 2y 10 ​ + y 1 ​ =2 ⇒ y 5 ​ + y 1 ​ =2 ⇒ y 6 ​ =2 ∴  y=3 ⇒  x=2y=2(3)=6

⇒  The two digit number =(10y+x)=10(3)+6=36

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## A Two Digit Number is 4 Times the Sum of Its Digits and Twice the Product of Its Digits. Find the Number.

A Two Digit Number is 4 Times the Sum of Its Digits and Twice the Product of Its Digits. Find the Number.

A two digit number is 4 times the sum of its digits and twice the product of its digits. Find the number.

### SOLUTION

Let the require digit be = (10x + y)

Then according to question

(10x + y) = 4(x + y)

(10x + y) = 4x + 4y

10x + y - 4x - 4y = 0

6x - 3y = 0 2x - y = 0

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

And, (10x + y) = 2xy                    .........(2)

Now putting the value of y in equation (2) from (1)

(10x + 2x) = (2x)(2x)

4x2 - 12x = 0 4x(x - 3) = 0 x(x - 3) = 0 So, either x = 0 Or x - 3 = 0 x = 3

So, the digit can never be negative.

When x = 3 then y = 2x = 2 x 3 = 6 Therefore, number =10x + y = 10(3) + 6 = 30 + 6 = 36

Thus, the required number be 36.

Concept: Solutions of Quadratic Equations by Factorization

Is there an error in this question or solution?

Chapter 4: Quadratic Equations - Exercise 4.7 [Page 52]

Q 27 Q 26 Q 28

### APPEARS IN

RD Sharma Class 10 Maths

Exercise 4.7 | Q 27 | Page 52

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## A two digit number is 4 times the sum of its digits and twice

Answer of Given that the sum of the digits

## . A two digit number is 4 times the sum of its digits and twice

the product of its digits.The number is - - - - - -

Explanation:

Let x be the digit in the ones place and y be the digit in the tens place, resulting in the two-digit number = 10 y + x..

Given that the sum of the digits of a two-digit integer equals four,

According to the question

,