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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.
Solution
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 ⇒ 10y + x = 4(x + y) ⇒ 10y + x = 4x + 4y ⇒ 3x – 6y = 0 ⇒ 3x = 6y ∴ 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
10/x + 1/y =2
put x =2y from 1, we get
6/y = 3
so y = 2 and hence x= 6 Hence x = 6
The two digit number is (10y + x) = 10(3) + 6 = 36
Mathematics
Secondary School Mathematics X
Standard X
15