Problems on Numbers Quiz Set 006

Let the numbers be a and b, and let their ratio be k such that $a/b = k$. We are given $a + b = 53$ ⇒ $b(k + 1) = 53$. Similarly, from the difference we can obtain $b(k - 1) = 15$. Dividing we get ${k + 1}/{k - 1} = 53/15$. By componendo and dividendo, $k = {53 + 15}/{53 - 15}$ = ${34/19}$, which is same as: $1{15/19}$.

Let the numbers be 2n - 3, 2n - 1 and 2n + 1. The sum is 3(2n - 1) = 3 x middle. We are given 3 x middle = -2211, ⇒ middle = $-2211/3$, i.e., middle = -737.

Odd numbers are in an AP. First term $a = -1713$, common difference $d = 2$, the last term $t_n$ is given as 2241. By the AP formula, $2241 = -1713 + (n - 1) × 2$ ⇒ $n = 1 + {{2241 - (-1713)}/2} = 1978$.

Let $x/7 = y/19 = z/24$ = k. Then ${x + y + z}/x$ is same as ${7k + 19k + 24k}/{7k}$ which equals $7{1/7}$.

${50/7}$ is same as $7{1/7}$.

Let the number be N. Then ${6/17}$ x N = 24. ⇒ N = 24 x ${17/6}$ = 68