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 ⇒ 2x − y = 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.MathematicsRS Aggarwal (2015)Standard X

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