Which information are sufficient to answer the questions? What is the mother’s present age? I. The present ages of mother and child are in the ratio of 5 : 1 respectively. II. Four years hence the ratio of the ages of mother and child will be 17 : 5 respectively.

Statement I gives ratio M:C = 5:1, but one equation with two unknowns is insufficient. Statement II gives (M+4):(C+4) = 17:5, also one equation with two unknowns - insufficient alone. Together they form two equations that can be solved: M = 5C and (5C+4)/(C+4) = 17/5, giving C = 6 and M = 30. Both statements together are necessary and sufficient.