ए टू डिजिट नंबर इज फोर टाइम्स द सम ऑफ इट्स डिजिट्स एंड twice द प्रोडक्ट ऑफ डिजिट फाइंड द नंबर
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Class 10
>>Maths
>>Quadratic Equations
>>Solutions of Quadratic Equations
>>A two digit number is 4 times the sum of
Question
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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 ------
Medium
Solution
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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