Consider a 2-digit number N. Let P be the product of the digits of the number. If P is added to square of the digit in the tens place of N, we get 84. If P is added to the square of the digit in the unit place of N, we get 60. What is the value of P + N?
A.100
B.110✓ Correct
C.115
D.120
Explanation
Let tens digit = a, units digit = b, so N = 10a + b, P = ab. Given: a² + ab = 84, so a(a + b) = 84. And b² + ab = 60, so b(a + b) = 60. Dividing: a/b = 84/60 = 7/5. So a = 7, b = 5 (single digits). Check: 7(7+5) = 84 ✓, 5(7+5) = 60 ✓. N = 75, P = 35. P + N = 35 + 75 = 110.
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