H.C.F. of two numbers is 13. If these two numbers are in the ratio of 15: 11, then find the numbers.

Question: H.C.F. of two numbers is 13. If these two numbers are in the ratio of 15: 11, then find the numbers.Solution:H.C.F. of two numbers = 13The numbers are in the ratio of 15 : 11Let the two numbers be 15y and 11yH.C.F. is the product of common factorsTherefore, H.C.F. is y. So y = 13The two numbers are:15y = 15 × 13 = 19511y = 11 × 13 = 143We can cross-check the answer using the trick. (Product of two numbers = Product of their H.C.F. and L.C.M.)Product of H.C.F. and L.C.M. = 13 × 2145 = 27885Product of two numbers = 195 × 143 = 27885Hence, the calculated answer is correct.