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

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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.

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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.

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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

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

Q 27 Q 26 Q 28

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RD Sharma Class 10 Maths

Chapter 4 Quadratic Equations

Exercise 4.7 | Q 27 | Page 52

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