Problems on Ages Quiz Set 005

Let the present age be x. Then $x = 315/{x - 6}$. At this stage a better option is that you try putting the given answers into this expression one by one. The other option is to simplify this expression into a quadratic equation $x × (x - 6)$ = 315. This can now be solved to give x = 21 years.

Let the ages be x and y. We are given x + y = 12, and xy = 35. Substituting in the identity $x^2 + y^2 = (x + y)^2 - 2 × xy$, we get $x^2 + y^2 = 12^2 - 2 × 35$ = 74.

Let the ages of P and Q be 29x and 59x. After 3 years the ratio would be ${29x + 3}/{59x + 3}$ = ${119/239}$. Solving, we get x = 4. So age of P = 29 × 4 = 116.

Clearly, the age of the mother is twice her daughter's present age. So the daughter's age today is 36/2 = 18 years. And, 5 years back the age of the daughter was 18 - 5 = 13 years.

Let their present ages be x and y. Then ${x - 4}/{y - 4} = $ ${13/27}$. Similarly, ${x + 3}/{y + 3} = $ ${10/17}$. Solving these equations for x and y, we get y = 31, and x = 17 years as the answer.