Problems on Numbers Quiz Set 015

We can see that $1{19/x}$ = ${81/14}$ × ${17/97}$. ⇒ ${1x + 19}/x$ = ${1377/1358}$ ⇒ x = 1358.

This is the general solution. Let the numbers be 2n - 2, 2n and 2n + 2. We are given 14 × 2n = 160 + 11 × (2n - 2).
⇒ 14 × 2n = 160 + 11 × 2n - 11 × 2.
⇒ 2n × (14 - 11) = 160 - 11 × 2, so 2n = ${160 - 11 × 2}/{14 - 11} = 46$

Let $x/2 = y/19 = z/28$ = k. Then ${x + y + z}/x$ is same as ${2k + 19k + 28k}/{2k}$ which equals $24{1/2}$.

${49/2}$ is same as $24{1/2}$.

Let the number be n. From the given conditions we have $6n + 21 = 13n - 84$. Rearranging we have $84 + 21 = 13n - 6n$, ⇒ $n = {84 + 21}/{13 - 6}$. So n = 15.

This is the general solution. Let the numbers be 2n - 2, 2n and 2n + 2. We are given 5 × 2n = 46 + 2 × (2n - 2).
⇒ 5 × 2n = 46 + 2 × 2n - 2 × 2.
⇒ 2n × (5 - 2) = 46 - 2 × 2, so 2n = ${46 - 2 × 2}/{5 - 2} = 14$