let

x = the present age of Mrs. West

y = the present age of her aunt

Mrs. West is 14 years younger than her aunt

x = y - 14

Mrs. West's age in years is as much below 60 as her aunt's age is over 40

60 - x = y - 40

by solving the system of equations

x = y - 14

60 - x = y - 40

we find

x = 43 years

y = 57 years

Mrs. West is 43 years old and her aunt is 57 years old.