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Question

A two-digit number is four times the sum of its digits and twice the product of its digits. Find the number.


Solution

Let the tens and the units digits of the required number be x and y​, respectively. 
Required number = (10x + y)
∴ 10x + y = 4(x + y)
⇒ 10x + y = 4x + 4y
⇒ 6x − 3y = 0
⇒ 2xy = 0  or  y = 2x           ....(i)
Again, we have:
10x + y = 2xy                          ....(ii)
On substituting y = 2x in (ii), we get:
10x + 2x = 2x(2x)
12x = 4x2
4x = 12
x = 3
On substituting x = 3 in (i), we get:
2 × 3 − y = 0
⇒  y = 6
∴ Number = (10x + y) = 10 × 3 + 6 = 30 + 6 = 36
Hence, the required number is 36.

Mathematics
RS Aggarwal (2015)
Standard X

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