Let x be the least number which when divided by 15,18, 20 and 27, the remainder in each case is 10 and x is a multiple of 31. What least number should be added to x to make it a perfect square?

Answer: Option A

L.C.M. of 15,18, 20, 27 = 540
x = 540K + 10

x = 540 × 4 + 10 = 2170
46² < 2170 > 47²
47² = 2209
To make perfect square = 2209 - 2170 = 39