Share
Notifications

View all notifications
Advertisement

A Two Digit Number is Such that the Product of the Digits is 16. When 54 is Subtracted from the Number the Digits Are Interchanged. Find the Number - Mathematics

Login
Create free account


      Forgot password?

Question

A two digit number is such that the product of the digits is 16. When 54 is subtracted from the number the digits are interchanged. Find the number

Solution

Let the two digits be:

Tens digits be x and units = 16/x

Number `=10x+16/x`

Number obtained by interchanging `=10xx16/x+x`

`rArr(10x+16/x)-(10xx16/x+x)=54`

`rArr10x+16/7-160/x+x=54`

⇒ 10x2 + 16 - 160 - x2 = 54x

⇒ 9x2 - 54x - 144 = 0

⇒ x2 - 6x - 16 = 0

⇒ x2 - 8x + 2x - 16 = 0

⇒ x(x - 8) + 2(x - 8) = 0

⇒ (x - 8)(x + 2) = 0

⇒ x - 8 = 0

⇒ x = 8

Or

⇒ x + 2 = 0

⇒ x = -2

But, a digit can never be negative, hence x = 8

Hence the required number `=10x+16/x=10(8)+16/8=80+2=82`

  Is there an error in this question or solution?
Advertisement

APPEARS IN

 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Ex. 4.7 | Q: 24 | Page no. 52
 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Ex. 4.7 | Q: 24 | Page no. 52
Advertisement
A Two Digit Number is Such that the Product of the Digits is 16. When 54 is Subtracted from the Number the Digits Are Interchanged. Find the Number Concept: Solutions of Quadratic Equations by Factorization.
Advertisement
View in app×