a two digit number is 4 times the sum of its digits and twice the product of its digits. find the number
Answers
Friend...
Let
the tens digit be x and the units digit be y.
Then
the two-digit number is (10x + y).
Given: Two-digit number = 4 times sum of its digits
⇒10x + y = 4(x + y)
⇒ 10x + y = 4x + 4y
⇒ 6x = 3y
⇒ x = y/2
… (1)
Given: Two-digit number = Twice the product of its digits
⇒ 10x + y = 2(xy)
⇒10x + y – 2xy = 0 … (2)
Substituting
X = y/2
from equation (1) in equation (2)
10 × y/2 + y - 2 × y /2 × y = 0
⇒5y + y – y2 = 0
⇒y2 – 6y = 0
⇒y (y – 6) = 0
⇒ y = 0 or y – 6 = 0
We reject
y = 0
because then
x would also be zero.
y = 6
Substituting this value of y in equation 1
X = 6 / 2 = 3
the required number is (10 × 3 + 6) =
36.
Thankyou
SOLUTION :
Let the digit at the tens and units place be x and y .
Two digit number = 10x + y
A T.Q
Number = 4(sum of the digits) & Number = 2(product of the digits)
10x + y = 4(x + y) And 10x + y = 2xy …………(1)
10x + y = 4x + 4y
10x - 4x = 4y - y
6x - 3y = 0
3(2x - y) = 0
2x - y = 0
2x = y ……………….(2)
Put this value of y in eq 1
10x + y = 2xy
10x + 2x = 2x(2x)
12x = 4x²
4x² - 12x = 0
4x(x - 3) = 0
4x = 0 or (x - 3) = 0
x = 0 or x = 3
Since, the given number is a two digit number so its tens digit cannot be zero ( x ≠ 0 )
Therefore , x = 3
Put this value of x in eq 2,
y = 2x
y = 2 (3)
y = 6
Required number = 10x + y
= 10(3) + 6
= 30 + 6
Required number = 36
Hence, the Required two digit number is 36 .
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