A two-digit number is 4 times the sum of its digits and twice the product of the digits.Find the number.
Answers
Given : A two-digit number is 4 times the sum of its digits and twice the product of the digits.
Solution:
Let the digit in the unit's place be x and the digit at the tens place be y.
Number = 10y + x
The number obtained by reversing the order of the digits is = 10x + y
ATQ :
Condition : 1
10y + x = 4(x + y)
10y + x = 4x + 4y
4x + 4y - 10y – x = 0
3x – 6y = 0
3(x – 2y) = 0
x – 2y = 0
x = 2y ……………(1)
Condition : 2
10y + x = 2xy…………..(2)
On Substituting the value of x in equation (2) we obtain :
10y + 2y = 2 × (2y) × y
12y = 4y²
4y2 – 12y = 0
4y(y – 3) = 0
y(y – 3) = 0
y = 0 or y = 3
On putting y = 0 in eq (1) we obtain :
x = 2y
x = 2 × 0
x = 0
On putting y = 3 in eq (1) we obtain :
x = 2y
x = 2 × 3
x = 6
x = 0 and y = 0 pair of solution does not give a two digit number.
From x = 6 and y = 3 we obtain a number :
Number = 10y + x = 10 × 3 + 6 = 30 + 6 = 36
Hence, the number is 36.
Hope this answer will help you…
Some more questions from this chapter :
A two-digit number is 4 more than 6 times the sum of its digits. If 18 is subtracted from the number, the digits are reversed. Find the number.
https://brainly.in/question/17181674
A two-digit number is 3 more than 4 times the sum of its digits. If 18 is added to the number, the digits are reversed. Find the number.
https://brainly.in/question/17181140
Answer:
Step-by-step explanation:
Solution :-
Let the ones place digit be x.
and tens place digit be y.
Number = 10y + x
According to the Question,
⇒ 10y + x = 4(x + y)
⇒ 10y + x = 4x + 4y
⇒ 3x − 6y = 0
⇒ x = 2y .... (i)
⇒ 10y + x = 2xy
Dividing both sides with xy, we get
⇒ 10/x + 1/y = 2
Putting the value of Eq (i), we get
⇒ 10/2y + 1/y = 2
⇒ 5/y + 1/y = 2
⇒ 6/y = 2
⇒ y = 6/2
⇒ y = 3
Putting y's value in Eq (i), we get
⇒ x = 2y
⇒ x = 2(3)
⇒ x = 6
Number = (10y + x) = 10(3) + 6 = 36