Problems on Ages Quiz Set 008

The ratio of ages of A and B is given as ${20/9}$, which is same as: $2{2/9}$. So we can write the present ages of A and B, respectively, as 20r and 9r years. 8 years later the age of A is $20r + 8 = 188$ which gives r = 9. The age of B, therefore, is 9r = 9 × 9 = 81 years.

Let the ages of P and Q be 29x and 40x. After 6 years the ratio would be ${29x + 6}/{40x + 6}$ = ${151/206}$. Solving, we get x = 5. So age of P = 29 × 5 = 145.

Let the ages of P and Q be 14x and 47x. After 6 years the ratio would be ${14x + 6}/{47x + 6}$ = ${5/16}$. Solving, we get x = 6. So age of P = 14 × 6 = 84.

Let the age of R be x. Then the age of Q is 3x, and that of P is 3x + 11. Adding the three ages, (3x + 11) + 3x + x = 53. Solving, we get x = 6. So the age of Q is 3x = 18 years.

Let the present age be x. Then $√(x - 10) + √(x + 10)$ = $√{2x}$. Squaring both sides, $(√(x - 10))^2 + (√(x + 10))^2 + 2√{x^2 - 10^2}$ = $2x$ which gives $x - 10 + x + 10 + 2√{x^2 - 10^2}$ = $2x$. Cancelling, and simplifying, $2√(x^2 - 100) = 0$, which leads to x = 10 years.