Problems on Numbers Quiz Set 009

Let the number be ab. When it is reversed and added to itself we get (10a + b) + (10b + a) = 11 × (a + b). We are given 110 = 11 × (a + b) ⇒ $a + b = 110 / 11 = 10$, so the digits are $a$ and $10 - a$. We are given their product as a × (10 - a) = 21, which is a quadratic expression that can be simplified to $(a - 7) × (3 - a) = 0$. So the number could be 73 or 37.

Let the numbers be a and b, and let their ratio be k such that $a/b = k$. We are given $a + b = 25$ ⇒ $b(k + 1) = 25$. Similarly, from the difference we can obtain $b(k - 1) = 19$. Dividing we get ${k + 1}/{k - 1} = 25/19$. By componendo and dividendo, $k = {25 + 19}/{25 - 19}$ = ${22/3}$, which is same as: $7{1/3}$.

Let the number be N. Then it is given that ${23/34}$ x N = 17. ⇒ N = 17 X ${34/23}$. ⇒ ${19/21}$ x N = ${19/21}$ x 17 X ${34/23}$ = ${10982/483}$.

${10982/483}$ is same as $22{356/483}$.

Let the numbers be $a$ and $24 - a$. We are given their product as a × (24 - a) = 143, which is a quadratic expression that can be simplified to $(a - 13) × (11 - a) = 0$. So the numbers could be 13 and 11.

Let the numbers be n - 1, n and n + 1. The sum is 3n. We are given 3n = -1113, ⇒ n = $-1113/3$, i.e., n = -371. So the smallest is -372.