Problems based on Numbers Test 2

Let the two-digit number be 10x + y, then
10x + y = 6(x + y)
⇒ 4x – 5y = 0 ...(i)
And also, 10(x –1) + (y – 2) = 7(x – 1 + y – 2)
⇒ 10x + y – 12 = 7x + 7y – 21
⇒ 3x – 6y = – 9
⇒ x – 2y = – 3 ...(ii)
Solving equations (i) & (ii) we get x = 5 and y = 4
Hence, number = 10 × 5 + 4 = 54