Problems on Ages Quiz Set 006

The ratio of ages of A and B is given as ${21/5}$, which is same as: $4{1/5}$. So we can write the present ages of A and B, respectively, as 21r and 5r years. 4 years later the age of A is $21r + 4 = 109$ which gives r = 5. The age of B, therefore, is 5r = 5 × 5 = 25 years.

If the age of my father is F, then my age is F - 31, so my younger sister's age is (F - 31) - 6, which is = F - 37. If my mother's age is M, then M = (my sister's age) + 18, i.e., M = (F - 37) + 18. We get F - M = 19 years.

This question can be solved directly also. The age of my father at the time of birth of my sister was 31 + 6 = 37. At the time my mother was 18 years. So the difference between their ages = 37 - 18 = 19 years.

Let the present age be x. Then $√(x - 7) + √(x + 7)$ = $√{2x}$. Squaring both sides, $(√(x - 7))^2 + (√(x + 7))^2 + 2√{x^2 - 7^2}$ = $2x$ which gives $x - 7 + x + 7 + 2√{x^2 - 7^2}$ = $2x$. Cancelling, and simplifying, $2√(x^2 - 49) = 0$, which leads to x = 7 years.

Let the ages be 2r and 17r. The younger is 2r. We have been given their sum. So (2 + 17)r = 38. Solving, we get r = 2. The younger is 2 × 2 = 4 years.

Let the present age be x. Then $1/{x + 8} + 1/{x - 8}$ = ${70/1161}$. 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 ${2x}/{x^2 - 64}$ = ${70/1161}$. This can now be solved to give x = 35 years.